Question

Is the following group either a quaternion group or $D_8$?

score 78 · Answer 1 · 2014-11-21 08:17:08

78

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Is the following group either a quaternion group or $D_8$?

Published on 21 Nov 2014 - 8:17

score 1.6k · Answer 2 · 2014-11-21 12:04:02

1.6k

Views

Product of all elements of a finite group with an unique element of order 2

Published on 21 Nov 2014 - 12:04

score 160 · Answer 3 · 2014-11-21 14:53:35

160

Views

$G$ is a primitive group

Published on 21 Nov 2014 - 14:53

score 321 · Answer 4 · 2014-11-21 18:35:48

321

Views

Find generators in GF(19)

Published on 21 Nov 2014 - 18:35

score 1.8k · Answer 5 · 2026-04-07 20:37:03

1.8k

Views

What is a conjugacy class of reflection?

Published on 07 Apr 2026 - 20:37

score 301 · Answer 6 · 2014-11-21 21:35:12

301

Views

$|G| + \frac{|G|}{\left|\langle a\rangle\right|} + \frac{|G|}{\left|\langle b\rangle\right|} + \frac{|G|}{\left|\langle ab\rangle\right|}$

Published on 21 Nov 2014 - 21:35

score 904 · Answer 7 · 2014-11-22 16:33:31

904

Views

If $G$ is a finite non-trivial group of odd order, it has an irreducible representation not realisable over the reals.

Published on 22 Nov 2014 - 16:33

score 305 · Answer 8 · 2026-04-06 16:59:11

305

Views

If the commutator of a finite group has order $2$, then the order of the group is divisible by $8$

Published on 06 Apr 2026 - 16:59

score 967 · Answer 9 · 2014-11-22 22:00:16

967

Views

Prove either $G=ST$ or |$G|\geq|S|+|T|$

Published on 22 Nov 2014 - 22:00

score 793 · Answer 10 · 2014-11-22 23:48:48

793

Views

The number of solutions of $x^n = e$ in a finite group is a multiple of n, whenever n divides the group order.

Published on 22 Nov 2014 - 23:48

score 1.8k · Answer 11 · 2014-11-23 01:35:22

1.8k

Views

Suppose that half of the elements of G have order 2 and the other half form a subgroup H of order n. Prove that H is an abelian subgroup of G.

Published on 23 Nov 2014 - 1:35

score 188 · Answer 12 · 2026-03-29 12:12:10

188

Views

Cyclic finite groups and their direct product

Published on 29 Mar 2026 - 12:12

score 35 · Answer 13 · 2014-11-23 17:59:51

35

Views

images of subgroups of $G = \mathbb{Z}_4 \times \mathbb{Z}_4$ in $G/G[2]$

Published on 23 Nov 2014 - 17:59

score 48 · Answer 14 · 2014-11-24 01:09:56

48

Views

Showing that $|Z(G)| = p$ and $G/Z(G) \simeq \mathbb{Z}_p \times \mathbb{Z}_p$ for finite p-groups with order $|G|=p^3$

Published on 24 Nov 2014 - 1:09

score 468 · Answer 15 · 2014-11-24 05:43:26

468

Views

Showing that $|N \cap Z(G)| > 1$ for normal subgroups of p-groups

Published on 24 Nov 2014 - 5:43

List Question

Is the following group either a quaternion group or $D_8$?

Product of all elements of a finite group with an unique element of order 2

$G$ is a primitive group

Find generators in GF(19)

What is a conjugacy class of reflection?

$|G| + \frac{|G|}{\left|\langle a\rangle\right|} + \frac{|G|}{\left|\langle b\rangle\right|} + \frac{|G|}{\left|\langle ab\rangle\right|}$

If $G$ is a finite non-trivial group of odd order, it has an irreducible representation not realisable over the reals.

If the commutator of a finite group has order $2$, then the order of the group is divisible by $8$

Prove either $G=ST$ or |$G|\geq|S|+|T|$

The number of solutions of $x^n = e$ in a finite group is a multiple of n, whenever n divides the group order.

Suppose that half of the elements of G have order 2 and the other half form a subgroup H of order n. Prove that H is an abelian subgroup of G.

Cyclic finite groups and their direct product

images of subgroups of $G = \mathbb{Z}_4 \times \mathbb{Z}_4$ in $G/G[2]$

Showing that $|Z(G)| = p$ and $G/Z(G) \simeq \mathbb{Z}_p \times \mathbb{Z}_p$ for finite p-groups with order $|G|=p^3$

Showing that $|N \cap Z(G)| > 1$ for normal subgroups of p-groups

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