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[原创]群论的一些基础知识
商集商群概念没问题。。。。 你的意思是三种都是商群S3/A3吗?我也样是这想的,所以我问“同时”。。。 就对这S3有这疑问。大群S4,S5,S6.的商群就不这样 因为S3中6个置换1,12,13,23,123,132, 2,3出现从形式上是一样的--可说是可互换---可S3和它的正规子群A3的形成的商群={A3,(12)A3},也可以是{A3,(13)A3},这麽说就有2个(或3个)不同商群了------虽然都同构,你看S3的置换群表,在同一个置换群表却只能={A3,(12)A3},如果是{A3,(13)A3},{A3,(23)A3}就不行,当然在S3的抽象群表中没问题,可置换群表不行,什麽原因? |
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[原创]群论的一些基础知识
同情!不要灰心!觉得英语比代数简单啊,专业英语吗?可不知怎麽安慰好。。。。 现在考研内幕很多,反正要能合导师的心才行---------要把导师当慈禧,学生当太监,女生呢,身体才是本钱 |
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[原创]群论的一些基础知识
能不能从除环和扩域方面理解啊。。。 交换代数没学,中文就那一本黄皮小薄本,翻了翻 交换有限可除结合代数基是交换有限可除结合代数基的子集,能成子域,域,扩域,还能理解 非交换有限可除结合代数基是交换有限可除结合代数基的子集,能成子域,域,扩域吗? 交换有限可除结合代数基是非交换有限可除结合代数基的子集,能成子域,域,扩域吗? |
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[原创]群论的一些基础知识
把图帖这,慢慢看 |
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[原创]群论的一些基础知识
再问个商群问题:下面图当S3/A3这商集可成商群S3/A3={A3,(12)A3};如果下图运算成立的同时,那商集S3/A3={A3,(13)A3}或商集S3/A3={A3,(23)A3}为何不成商群? 再问个商群问题:下面图当S3/A3这商集可成商群S3/A3={A3,(12)A3};如果下图运算成立的同时,那商集S3/A3={A3,(13)A3}或商集S3/A3={A3,(23)A3}为何不成商群? 两抽象表: 1 B C D E A 1 B C D E A B D E 1 A C C E 1 A B D D 1 A B C E E A B C D 1 A C D E 1 B $ 0 2 3 4 5 1 The Group Z6 1 A B C D E 1 A B C D E A B 1 D E C B 1 A E C D C E D 1 B A D C E A 1 B E D C B A 1 $ R0 R240 R120 F1 F2 F3 The Dihedral Group D_3 The Group of Symmetries of an Equilateral Triangle. The Rx denotes clockwise rotation by x degrees and Fi a flip about vertex i. (Vertices are numbered clockwise) |
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[转帖] bin Laden is dead
究竞是什麽? |
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[转帖] bin Laden is dead
Программное обеспечение выпуска и Windows Crack Обучение Нам-Dabei Guanyin Бодхисаттва Нам без митабха GOOGLE:将英语译成中文(简体) Программноеобеспечениевыпускаи视窗裂纹Обучение Нам-大悲观音БодхисаттваНамбезмитабха Программное обеспечение выпуска и Windows Crack Обучение Нам-Dabei Guanyin Бодхисаттва Нам без митабха 将俄语译成中文(简体) 软件版本和Windows裂纹教育 美大悲观音菩萨我们没有mitabha Программное обеспечение выпуска и Windows Crack Обучение Нам-Dabei Guanyin Бодхисаттва Нам без митабха 将俄语译成英语 Software release and Windows Crack Education Us-Dabei Guanyin Bodhisattva us without mitabha Software release and Windows Crack Education Us-Dabei Guanyin Bodhisattva us without mitabha |
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一套内衣400万,我的神啊!
两老太太,长沙没身材好点的吗 |
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[转帖][分享]DES的群论性质及其分析
太难了。。。 |
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[原创]群论的一些基础知识
z:=IntegerRing(120); z; UnitGroup(z); zz:=IntegerRing(); zz; ClassGroup(zz) ; Signature(zz) ; sub< z | 2 >; sub< zz | 2 >; szz3:=sub< zz | 3 >; sz3:=sub< z | 3 >; sz6:=sub< z | 6 >; szz6:=sub< zz | 6 >; Characteristic(z) ; Characteristic(zz) ; Characteristic(sz3) ; Characteristic(szz3) ; IsUnitary(z); IsUnitary(zz); IsUnitary(szz3); IsUnitary(sz3); IsEuclideanDomain(z) ; IsEuclideanDomain(zz) ; IsEuclideanDomain(szz3) ; IsEuclideanDomain(sz3) ; IsEuclideanDomain(sz6); IsEuclideanDomain(szz6); IsPID(z); IsPID(zz); IsPID(sz3); IsPID(szz3); IsPID(sz6); IsPID(szz6); IsUFD(z); IsUFD(zz); IsUFD(sz3); IsUFD(szz3); IsUFD(sz6); IsUFD(szz6); IsEuclideanRing(z) ; IsEuclideanRing(zz) ; IsEuclideanRing(szz3) ; IsEuclideanRing(sz3) ; IsEuclideanRing(szz6) ; IsEuclideanRing(sz6) ; IsPrincipalIdealRing(z); IsPrincipalIdealRing(zz); IsPrincipalIdealRing(sz3); IsPrincipalIdealRing(szz3); IsPrincipalIdealRing(sz6); IsPrincipalIdealRing(szz6); Modulus(sz3) ; Modulus(sz6) ; Residue class ring of integers modulo 120 Abelian Group isomorphic to Z/2 + Z/2 + Z/2 + Z/4 Defined on 4 generators Relations: 2*$.1 = 0 2*$.2 = 0 2*$.3 = 0 4*$.4 = 0 Integer Ring Abelian Group of order 1 1 0 Ideal of residue class ring of integers modulo 120 generated by 2 Ideal of Integer Ring generated by 2 Mapping from: Ideal of Integer Ring generated by 2 to RngInt: zz 120 0 120 0 true true false false false true true false false true false true false true false true false true false true false true true true true true true true true true true true true true 120 120 http://jsjxy.cug.edu.cn/jxkj/ma/jiaoan/L1%20algebra.pdf http://zh.wikipedia.org/wiki/%E4%B8%BB%E7%90%86%E6%83%B3%E7%92%B0 |
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[原创]群论的一些基础知识
z:=IntegerRing(15); z; UnitGroup(z); zz:=IntegerRing(); zz; ClassGroup(zz) ; Signature(zz) ; sub< z | 2 >; sub< zz | 2 >; szz3:=sub< zz | 3 >; sz3:=sub< z | 3 >; sz6:=sub< z | 6 >; szz6:=sub< zz | 6 >; Characteristic(z) ; Characteristic(zz) ; Characteristic(sz3) ; Characteristic(szz3) ; IsUnitary(z); IsUnitary(zz); IsUnitary(szz3); IsUnitary(sz3); IsEuclideanDomain(z) ; IsEuclideanDomain(zz) ; IsEuclideanDomain(szz3) ; IsEuclideanDomain(sz3) ; IsEuclideanDomain(sz6); IsEuclideanDomain(szz6); IsPID(z); IsPID(zz); IsPID(sz3); IsPID(szz3); IsPID(sz6); IsPID(szz6); IsUFD(z); IsUFD(zz); IsUFD(sz3); IsUFD(szz3); IsUFD(sz6); IsUFD(szz6); IsEuclideanRing(z) ; IsEuclideanRing(zz) ; IsEuclideanRing(szz3) ; IsEuclideanRing(sz3) ; IsEuclideanRing(szz6) ; IsEuclideanRing(sz6) ; IsPrincipalIdealRing(z); IsPrincipalIdealRing(zz); IsPrincipalIdealRing(sz3); IsPrincipalIdealRing(szz3); IsPrincipalIdealRing(sz6); IsPrincipalIdealRing(szz6); Residue class ring of integers modulo 15 Abelian Group isomorphic to Z/2 + Z/4 Defined on 2 generators Relations: 2*$.1 = 0 4*$.2 = 0 Integer Ring Abelian Group of order 1 1 0 Residue class ring of integers modulo 15 Ideal of Integer Ring generated by 2 Mapping from: Ideal of Integer Ring generated by 2 to RngInt: zz 15 0 15 0 true true false false false true true false false true false true false true false true false true false true false true true true true true true true true true true true true true |
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[原创]群论的一些基础知识
P:=PermutationGroup< 6 | (1,2,4) >; P; Orbits(P); P1:=PermutationGroup< 7 | (3,2,4,1) >; P1; Orbits(P1); P2:=PermutationGroup< 8 | (2,4,7,3,5,6) >; P2; Orbits(P2); Stabilizer(P, 1); Stabilizer(P1, 6); Stabilizer(P1, 5); Stabilizer(P2, 8); Permutation group P acting on a set of cardinality 6 (1, 2, 4) [ GSet{@ 3 @}, GSet{@ 5 @}, GSet{@ 6 @}, GSet{@ 1, 2, 4 @} ] Permutation group P1 acting on a set of cardinality 7 (1, 3, 2, 4) [ GSet{@ 5 @}, GSet{@ 6 @}, GSet{@ 7 @}, GSet{@ 1, 3, 2, 4 @} ] Permutation group P2 acting on a set of cardinality 8 (2, 4, 7, 3, 5, 6) [ GSet{@ 1 @}, GSet{@ 8 @}, GSet{@ 2, 4, 7, 3, 5, 6 @} ] Permutation group acting on a set of cardinality 6 Order = 1 Permutation group P1 acting on a set of cardinality 7 Order = 4 = 2^2 (1, 3, 2, 4) Permutation group P1 acting on a set of cardinality 7 Order = 4 = 2^2 (1, 3, 2, 4) Permutation group P2 acting on a set of cardinality 8 Order = 6 = 2 * 3 (2, 4, 7, 3, 5, 6) |
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[转帖]国家安全局副局长名单
副局长名单保密,说肯定有副文化部长一名 |
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[原创]群论的一些基础知识
谢!越来越难。。。 不过先问简单的群在集合上的作用,一般都考虑|G|=|X|,可也可以不相等,居然还有群在群作用,这些作用就是群表示吗? P:=PermutationGroup< 3 | (1,2) >; P; GSet(P); SET:={1,2,3}; SET; GS:=GSet(P, SET) ; GS; Action(GS) ; Group(GS); Support(P); Support(P, GS) ; Orbit(P, GS, 1) ; Orbit(P, GS, 2) ; Orbit(P, GS, 3) ; Orbits(P, GS) ; Orbit(P, 1) ; Orbit(P, 2) ; Orbit(P, 3) ; Orbits(P) ; Stabilizer(P, GS, 1) ; Stabilizer(P, GS, 2) ; Stabilizer(P, GS, 3) ; Stabilizer(P, GS) ; Stabilizer(P, 1) ; Stabilizer(P, 2) ; Stabilizer(P, 3) ; Stabiliser(P, 1); Stabiliser(P, 3); Transitivity(P) ; Transitivity(P, GS) ; IsPrimitive(P, GS) ; IsTransitive(P, GS) ; IsFrobenius(P) ; Stabilizer(P, [1,2]); Stabilizer(P, [3,2]); Stabilizer(P, [1,3]); Stabilizer(P, [1,2,3]); Stabilizer(P, [[1],[2]]); Stabilizer(P, [1,2,0]); Orbit(P, [1,2,3]) ; Action(P, GS) ; Permutation group P acting on a set of cardinality 3 (1, 2) GSet{@ 1, 2, 3 @} { 1, 2, 3 } GSet{@ 1, 2, 3 @} Mapping from: Cartesian Product<{@ 1, 2, 3 @}, GrpPerm: P, Degree 3> to {@ 1, 2, 3 @} Permutation group P acting on a set of cardinality 3 (1, 2) { 1, 2 } { 1, 2 } GSet{@ 1, 2 @} GSet{@ 2, 1 @} GSet{@ 3 @} [ GSet{@ 3 @}, GSet{@ 1, 2 @} ] GSet{@ 1, 2 @} GSet{@ 2, 1 @} GSet{@ 3 @} [ GSet{@ 3 @}, GSet{@ 1, 2 @} ] Permutation group acting on a set of cardinality 3 Order = 1 Permutation group acting on a set of cardinality 3 Order = 1 Permutation group acting on a set of cardinality 3 Order = 2 (1, 2) Permutation group acting on a set of cardinality 3 Order = 2 (1, 2) Permutation group acting on a set of cardinality 3 Order = 1 Permutation group acting on a set of cardinality 3 Order = 1 Permutation group P acting on a set of cardinality 3 Order = 2 (1, 2) Permutation group acting on a set of cardinality 3 Order = 1 Permutation group P acting on a set of cardinality 3 Order = 2 (1, 2) 0 0 false false false Permutation group acting on a set of cardinality 3 Order = 1 Permutation group acting on a set of cardinality 3 Order = 1 Permutation group acting on a set of cardinality 3 Order = 1 Permutation group acting on a set of cardinality 3 Order = 1 Permutation group acting on a set of cardinality 3 Order = 1 >> Stabilizer(P, [1,2,0]); ^ Runtime error in 'Stabilizer': Cannot compute stabilizer of this object GSet{@ [ 1, 2, 3 ], [ 2, 1, 3 ] @} Mapping from: GrpPerm: P to GrpPerm: $, Degree 3 P:=PermutationGroup< 5 | (1,2,4) >; P; GSet(P); SET:={1,2,3,4,5}; SET; GS:=GSet(P, SET) ; GS; Action(GS) ; Group(GS); Support(P); Support(P, GS) ; Orbit(P, GS, 1) ; Orbit(P, GS, 2) ; Orbit(P, GS, 3) ; Orbits(P, GS) ; Orbit(P, 1) ; Orbit(P, 2) ; Orbit(P, 3) ; Orbits(P) ; Stabilizer(P, GS, 1) ; Stabilizer(P, GS, 2) ; Stabilizer(P, GS, 3) ; Stabilizer(P, GS) ; Stabilizer(P, 1) ; Stabilizer(P, 2) ; Stabilizer(P, 3) ; Stabiliser(P, 1); Stabiliser(P, 3); Transitivity(P) ; Transitivity(P, GS) ; IsPrimitive(P, GS) ; IsTransitive(P, GS) ; IsFrobenius(P) ; Stabilizer(P, [1,2]); Stabilizer(P, [3,2]); Stabilizer(P, [1,3]); Stabilizer(P, [1,2,3]); Stabilizer(P, [[1],[2]]); Stabilizer(P, [1,2,0]); Orbit(P, [1,2,3]) ; Action(P, GS) ; Permutation group P acting on a set of cardinality 5 (1, 2, 4) GSet{@ 1, 2, 3, 4, 5 @} { 1, 2, 3, 4, 5 } GSet{@ 1, 2, 3, 4, 5 @} Mapping from: Cartesian Product<{@ 1, 2, 3, 4, 5 @}, GrpPerm: P, Degree 5> to {@ 1, 2, 3, 4, 5 @} Permutation group P acting on a set of cardinality 5 (1, 2, 4) { 1, 2, 4 } { 1, 2, 4 } GSet{@ 1, 2, 4 @} GSet{@ 2, 4, 1 @} GSet{@ 3 @} [ GSet{@ 3 @}, GSet{@ 5 @}, GSet{@ 1, 2, 4 @} ] GSet{@ 1, 2, 4 @} GSet{@ 2, 4, 1 @} GSet{@ 3 @} [ GSet{@ 3 @}, GSet{@ 5 @}, GSet{@ 1, 2, 4 @} ] Permutation group acting on a set of cardinality 5 Order = 1 Permutation group acting on a set of cardinality 5 Order = 1 Permutation group acting on a set of cardinality 5 Order = 3 (1, 2, 4) Permutation group acting on a set of cardinality 5 Order = 3 (1, 2, 4) Permutation group acting on a set of cardinality 5 Order = 1 Permutation group acting on a set of cardinality 5 Order = 1 Permutation group P acting on a set of cardinality 5 Order = 3 (1, 2, 4) Permutation group acting on a set of cardinality 5 Order = 1 Permutation group P acting on a set of cardinality 5 Order = 3 (1, 2, 4) 0 0 false false false Permutation group acting on a set of cardinality 5 Order = 1 Permutation group acting on a set of cardinality 5 Order = 1 Permutation group acting on a set of cardinality 5 Order = 1 Permutation group acting on a set of cardinality 5 Order = 1 Permutation group acting on a set of cardinality 5 Order = 1 >> Stabilizer(P, [1,2,0]); ^ Runtime error in 'Stabilizer': Cannot compute stabilizer of this object GSet{@ [ 1, 2, 3 ], [ 2, 4, 3 ], [ 4, 1, 3 ] @} Mapping from: GrpPerm: P to GrpPerm: $, Degree 5 |
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[求助]关于暴力破解des的密钥。
穷举,DES有个简化版,可以试用WSHARK看看DES过程,要从正规DES解密----变种很多,那还是看看电子前沿基金会http://www.eff.org/,,2^56微机不行,大型机也不是一下就行的 |
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[原创]群论的一些基础知识
K := FiniteField(5); > GL := GeneralLinearGroup(4, K); > GL ; x:= elt<GL | 5,6,1, 2,1,4, 11,10,1, 3,4,5, 4,5,6, 6>; > x; m := MatrixGroup< 3, K | [1,3,2, 23,1,2, 1,5^2,1], [2,0,0, 14,1,10, 10,0,33] >; m; O1:=Order(GL); FactoredOrder(GL); O2:=Order(m); FactoredOrder(m); Generic(GL); Parent(GL); Generic(m); Parent(m); CoefficientRing(GL); CoefficientRing(m); Generators(GL); Generators(m); NumberOfGenerators(GL); NumberOfGenerators(m); Degree(GL); Degree(m); RSpace(GL) ; RSpace(m) ; VectorSpace(GL); VectorSpace(m); GModule(GL) ; GModule(m) ; GL(4, GF(5)) [0 1 1 2] [1 4 1 0] [1 3 4 0] [4 0 1 1] MatrixGroup(3, GF(5)) Generators: [1 3 2] [3 1 2] [1 0 1] [2 0 0] [4 1 0] [0 0 3] [ <2, 11>, <3, 2>, <5, 6>, <13, 1>, <31, 1> ] [ <2, 5>, <3, 1>, <5, 3>, <31, 1> ] MatrixGroup(4, GF(5)) of order 2^11 * 3^2 * 5^6 * 13 * 31 Generators: [2 0 0 0] [0 1 0 0] [0 0 1 0] [0 0 0 1] [4 0 0 1] [4 0 0 0] [0 4 0 0] [0 0 4 0] Power Structure of GrpMat GL(3, GF(5)) Power Structure of GrpMat Finite field of size 5 Finite field of size 5 { [2 0 0 0] [0 1 0 0] [0 0 1 0] [0 0 0 1], [4 0 0 1] [4 0 0 0] [0 4 0 0] [0 0 4 0] } { [2 0 0] [4 1 0] [0 0 3], [1 3 2] [3 1 2] [1 0 1] } 2 2 4 3 Full Vector space of degree 4 over GF(5) Full Vector space of degree 3 over GF(5) Full Vector space of degree 4 over GF(5) Full Vector space of degree 3 over GF(5) GModule of dimension 4 over GF(5) GModule of dimension 3 over GF(5) |
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[原创]群论的一些基础知识
谢! 其实我想问的有限生成交换群的RANK 和线性代数里的RANK的区别,您再给说说, 你给公式rankH=rankK+rank(H/K)适用于有限生成交换群秩,极大无关组中向量的个数为非交换线性代数的秩的有没公式? 华罗庚据说是体大师。。。。 体、斜域,区,都有翻译的问题,就像同态(映射),让人迷糊,】 复数域是Q的子域,书上定义只用了a+bi+cj+dk四个单位中的2项:a+bi的复数域是Q的a1+bi的子域,不好懂。。。 |
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