Question

$\operatorname{Aut}(\mathbb{Z}_2 \times \mathbb{Z}_2) \cong \mathbb{Z}_2$

score 1k · Answer 1 · 2018-06-21 04:14:51

1k

Views

$\operatorname{Aut}(\mathbb{Z}_2 \times \mathbb{Z}_2) \cong \mathbb{Z}_2$

Published on 21 Jun 2018 - 4:14

score 95 · Answer 2 · 2018-06-21 11:25:29

95

Views

$U(p^m) \times U(q^n)$ is not cyclic

Published on 21 Jun 2018 - 11:25

score 336 · Answer 3 · 2026-03-25 04:43:30

336

Views

Does the list of "number of groups of order $n$" contain every natural number?

Published on 25 Mar 2026 - 4:43

score 504 · Answer 4 · 2026-03-25 03:04:15

504

Views

How to prove: if $G$ finite, $P$ a subgroup or order $p$ and $P = C_G(P)$ then $P$ is a Sylow $p$-subgroup of $G$

Published on 25 Mar 2026 - 3:04

score 336 · Answer 5 · 2018-06-23 14:01:25

336

Views

Possible order of an element in a group

Published on 23 Jun 2018 - 14:01

score 40 · Answer 6 · 2018-06-24 17:17:12

40

Views

Reference request for a theorem of Brauer regarding representations of a finite group

Published on 24 Jun 2018 - 17:17

score 99 · Answer 7 · 2018-06-25 02:16:40

99

Views

Number of elements of order $m$ in the symmetric group $S_m$

Published on 25 Jun 2018 - 2:16

score 841 · Answer 8 · 2018-06-25 03:02:11

841

Views

Let $H$ be a normal subgroup of a finite group $G$ and $x \in G$. Show that if the greatest common divisor $(| x |, | H |) = 1$ , then $x \in H$.

Published on 25 Jun 2018 - 3:02

score 78 · Answer 9 · 2018-06-26 16:39:42

78

Views

If $H<G$ are finite groups, must there be a way to realize them as permutation groups such that $H$ is not transitive?

Published on 26 Jun 2018 - 16:39

score 219 · Answer 10 · 2018-06-26 21:06:47

219

Views

A question regarding the proof of G a finite group, H a subgroup then $\left|G\right| = \left|G/H\right|\cdot \left|H\right| $

Published on 26 Jun 2018 - 21:06

score 128 · Answer 11 · 2018-06-27 06:36:45

128

Views

Showing the existence of an element $g \in G$, a finite abelian group, where $g$ has order $LCM\{|x|: x \in G\}$

Published on 27 Jun 2018 - 6:36

score 258 · Answer 12 · 2026-03-26 14:42:50

258

Views

The order of Orthogonal group $O^{-}(2,q)$

Published on 26 Mar 2026 - 14:42

score 5.9k · Answer 13 · 2018-06-27 18:43:21

5.9k

Views

Representations and classes of square group (D4)

Published on 27 Jun 2018 - 18:43

score 378 · Answer 14 · 2018-06-27 20:22:33

378

Views

Which group of order 24 is this group?

Published on 27 Jun 2018 - 20:22

score 132 · Answer 15 · 2026-03-26 09:45:52

132

Views

Isomorphically comparing normal subgroups and their quotient groups

Published on 26 Mar 2026 - 9:45

List Question

$\operatorname{Aut}(\mathbb{Z}_2 \times \mathbb{Z}_2) \cong \mathbb{Z}_2$

$U(p^m) \times U(q^n)$ is not cyclic

Does the list of "number of groups of order $n$" contain every natural number?

How to prove: if $G$ finite, $P$ a subgroup or order $p$ and $P = C_G(P)$ then $P$ is a Sylow $p$-subgroup of $G$

Possible order of an element in a group

Reference request for a theorem of Brauer regarding representations of a finite group

Number of elements of order $m$ in the symmetric group $S_m$

Let $H$ be a normal subgroup of a finite group $G$ and $x \in G$. Show that if the greatest common divisor $(| x |, | H |) = 1$ , then $x \in H$.

If $H<G$ are finite groups, must there be a way to realize them as permutation groups such that $H$ is not transitive?

A question regarding the proof of G a finite group, H a subgroup then $\left|G\right| = \left|G/H\right|\cdot \left|H\right| $

Showing the existence of an element $g \in G$, a finite abelian group, where $g$ has order $LCM\{|x|: x \in G\}$

The order of Orthogonal group $O^{-}(2,q)$

Representations and classes of square group (D4)

Which group of order 24 is this group?

Isomorphically comparing normal subgroups and their quotient groups

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