Question

proving Caley's Theorm using the conjugacy operation instead of left multiplication

score 42 · Answer 1 · 2026-04-01 11:36:21

42

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proving Caley's Theorm using the conjugacy operation instead of left multiplication

Published on 01 Apr 2026 - 11:36

score 424 · Answer 2 · 2015-07-14 21:37:47

424

Views

Understanding isomorphisms (abstract algebra)

Published on 14 Jul 2015 - 21:37

score 582 · Answer 3 · 2015-07-23 00:59:39

582

Views

Every isomorphism of subgroups of $\mathbb{Q}$ is of the form $\varphi(x)=qx$ for some $q \in \mathbb{Q}$.

Published on 23 Jul 2015 - 0:59

score 160 · Answer 4 · 2015-07-24 11:45:48

160

Views

Prove $K\cong S_3$

Published on 24 Jul 2015 - 11:45

score 121 · Answer 5 · 2026-03-29 02:54:42

121

Views

Operation $\circ$ on $\mathbb{R}: x\circ y=x\sqrt{1+y^2}+y\sqrt{1+x^2}$

Published on 29 Mar 2026 - 2:54

score 1k · Answer 6 · 2026-03-30 05:32:21

1k

Views

Sylow Theorems to find all groups with order less than or equal to 10

Published on 30 Mar 2026 - 5:32

score 49 · Answer 7 · 2026-04-02 00:12:07

49

Views

A question about Inner and outer Automorphism

Published on 02 Apr 2026 - 0:12

score 190 · Answer 8 · 2015-08-07 18:11:07

190

Views

General Isomorphism, for all algebraic structures

Published on 07 Aug 2015 - 18:11

score 107 · Answer 9 · 2026-03-29 19:51:26

107

Views

group of Automorphisms

Published on 29 Mar 2026 - 19:51

score 130 · Answer 10 · 2015-08-13 18:22:23

130

Views

Not understanding the case where $G$ is abelian with every element of order $2$

Published on 13 Aug 2015 - 18:22

score 54 · Answer 11 · 2015-08-18 17:03:41

54

Views

$ G = MC $ for some cyclic subgroup $ C $. If $ \vert G : M \vert = 4 $ then why $ G \cong S_{4} $?

Published on 18 Aug 2015 - 17:03

score 264 · Answer 12 · 2015-08-20 20:24:14

264

Views

Let $G$ be a group such that $|G| \ge 3$ then $|AutG| \ge 2$.

Published on 20 Aug 2015 - 20:24

score 84 · Answer 13 · 2026-03-27 00:10:10

84

Views

Let $ K/L $ be a chief factor of $ G $ and $ M $ be the smallest normal subgroup of $ K $ such that $ K/M $ is nilpotent

Published on 27 Mar 2026 - 0:10

score 79 · Answer 14 · 2026-03-27 06:12:34

79

Views

For any $n>1$ , $ Aut(\mathbb Z^n) \cong GL(n , \mathbb Z)$ ? And for any $m,n >1$ , $Aut(\mathbb Z_m ^n) \cong GL(n , \mathbb Z_m)$ ?

Published on 27 Mar 2026 - 6:12

score 1.9k · Answer 15 · 2015-08-27 06:03:01

1.9k

Views

Show that $\langle x,y\mid xyx=yxy,x^3=y^2\rangle\cong\{e\}$.

Published on 27 Aug 2015 - 6:03

List Question

proving Caley's Theorm using the conjugacy operation instead of left multiplication

Understanding isomorphisms (abstract algebra)

Every isomorphism of subgroups of $\mathbb{Q}$ is of the form $\varphi(x)=qx$ for some $q \in \mathbb{Q}$.

Prove $K\cong S_3$

Operation $\circ$ on $\mathbb{R}: x\circ y=x\sqrt{1+y^2}+y\sqrt{1+x^2}$

Sylow Theorems to find all groups with order less than or equal to 10

A question about Inner and outer Automorphism

General Isomorphism, for all algebraic structures

group of Automorphisms

Not understanding the case where $G$ is abelian with every element of order $2$

$ G = MC $ for some cyclic subgroup $ C $. If $ \vert G : M \vert = 4 $ then why $ G \cong S_{4} $?

Let $G$ be a group such that $|G| \ge 3$ then $|AutG| \ge 2$.

Let $ K/L $ be a chief factor of $ G $ and $ M $ be the smallest normal subgroup of $ K $ such that $ K/M $ is nilpotent

For any $n>1$ , $ Aut(\mathbb Z^n) \cong GL(n , \mathbb Z)$ ? And for any $m,n >1$ , $Aut(\mathbb Z_m ^n) \cong GL(n , \mathbb Z_m)$ ?

Show that $\langle x,y\mid xyx=yxy,x^3=y^2\rangle\cong\{e\}$.

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