Question

Let $G$ be a group, and the order of the group $G$, $|G|=r$. For any $x \in G$, prove that $x^{-r}=e$ (where $e$ is a neutral in $G$).

score 352 · Answer 1 · 2018-11-20 22:19:42

352

Views

Let $G$ be a group, and the order of the group $G$, $|G|=r$. For any $x \in G$, prove that $x^{-r}=e$ (where $e$ is a neutral in $G$).

Published on 20 Nov 2018 - 22:19

score 271 · Answer 2 · 2026-03-27 10:44:47

271

Views

Problem involving $\mathbb{Z} /63 \mathbb{Z}$ and its subgroups.

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score 218 · Answer 3 · 2018-11-21 07:58:30

218

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Schur multiplier of direct product

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1.7k

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Symmetry group of equilateral triangle

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score 25 · Answer 5 · 2018-11-21 09:19:58

25

Views

How to proof that $G$ and $G^*$ has the same number of generators?

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score 416 · Answer 6 · 2018-11-22 07:33:52

416

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score 341 · Answer 7 · 2026-03-25 22:03:36

341

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Is $G$ isomorphic to the dihedral group $D_{10}$?

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score 109 · Answer 8 · 2026-03-25 06:12:17

109

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Subgroups of $G^n$, where $G$ is a $p$-group

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score 198 · Answer 9 · 2018-11-22 13:03:52

198

Views

Show that finite simple group $G$ with $n$ involutions satisfies $n < |G| / 3$

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score 153 · Answer 10 · 2026-03-25 12:50:55

153

Views

$x,y \in Z_G(P)$ such that $gxg^{-1}=y$, show that there exists $n\in N_G(P)$ such that $nxn^{-1}=y$.

Published on 25 Mar 2026 - 12:50

score 571 · Answer 11 · 2026-03-25 08:12:12

571

Views

Coxeter length in the symmetric group equals number of inversions

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score 123 · Answer 12 · 2018-11-24 14:46:09

123

Views

Let $G$ be a finite group with a normal subgroup $H$ such that $G/H$ has order 7. $G$ is isomorphic to $ H × G/H$ .

Published on 24 Nov 2018 - 14:46

score 290 · Answer 13 · 2026-03-25 14:27:07

290

Views

Diameter of Cayley graphs of symmetric groups

Published on 25 Mar 2026 - 14:27

score 310 · Answer 14 · 2026-03-24 22:09:44

310

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Can every finite group be presented as an Fp group?

Published on 24 Mar 2026 - 22:09

score 93 · Answer 15 · 2018-11-26 10:47:44

93

Views

On groups with $\operatorname{Inn}(G) \cong D_8$ or $A_4$.

Published on 26 Nov 2018 - 10:47

List Question

Let $G$ be a group, and the order of the group $G$, $|G|=r$. For any $x \in G$, prove that $x^{-r}=e$ (where $e$ is a neutral in $G$).

Problem involving $\mathbb{Z} /63 \mathbb{Z}$ and its subgroups.

Schur multiplier of direct product

Symmetry group of equilateral triangle

How to proof that $G$ and $G^*$ has the same number of generators?

Prove there is only one subgroup of order $p$

Is $G$ isomorphic to the dihedral group $D_{10}$?

Subgroups of $G^n$, where $G$ is a $p$-group

Show that finite simple group $G$ with $n$ involutions satisfies $n < |G| / 3$

$x,y \in Z_G(P)$ such that $gxg^{-1}=y$, show that there exists $n\in N_G(P)$ such that $nxn^{-1}=y$.

Coxeter length in the symmetric group equals number of inversions

Let $G$ be a finite group with a normal subgroup $H$ such that $G/H$ has order 7. $G$ is isomorphic to $ H × G/H$ .

Diameter of Cayley graphs of symmetric groups

Can every finite group be presented as an Fp group?

On groups with $\operatorname{Inn}(G) \cong D_8$ or $A_4$.

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