Question

The Lemma for sylow theorem. show that prime $p$ divides $|X|-|X_G|$

score 36 · Answer 1 · 2016-09-28 06:23:10

36

Views

The Lemma for sylow theorem. show that prime $p$ divides $|X|-|X_G|$

Published on 28 Sep 2016 - 6:23

score 1.3k · Answer 2 · 2026-03-25 06:13:08

1.3k

Views

Understanding the wreath product of $\mathbb Z_2$ by $\mathbb Z_2$ and of $\mathbb Z_2$ by $\mathbb Z_3$

Published on 25 Mar 2026 - 6:13

score 1.6k · Answer 3 · 2016-10-04 15:47:42

1.6k

Views

$|G|=p(p+1)$ for $p$ prime, then $G$ has a normal subgroup of order $p$ or $p+1$

Published on 04 Oct 2016 - 15:47

score 154 · Answer 4 · 2016-10-05 06:03:59

154

Views

Why is it that every 2-Sylow subgroup of G is cyclic?

Published on 05 Oct 2016 - 6:03

score 117 · Answer 5 · 2016-10-05 12:16:07

117

Views

Cyclic groups of order $pq$ proof question

Published on 05 Oct 2016 - 12:16

score 51 · Answer 6 · 2016-10-06 11:46:23

51

Views

Show that $|K_{2,5}|=60.$

Published on 06 Oct 2016 - 11:46

score 452 · Answer 7 · 2016-10-07 15:13:23

452

Views

Proof explanation on a group of order $595$ having a normal Sylow $17$-subgroup.

Published on 07 Oct 2016 - 15:13

score 421 · Answer 8 · 2016-10-08 19:17:30

421

Views

Is my proof correct? Let $G$ be a group of order $10989$. Prove that $G$ contains either a normal Sylow $37$-subgroup or a normal Sylow $3$-subgroup

Published on 08 Oct 2016 - 19:17

score 352 · Answer 9 · 2016-10-18 00:45:37

352

Views

Proof of the first Sylow theorem in the Artin's textbook

Published on 18 Oct 2016 - 0:45

score 58 · Answer 10 · 2016-10-18 05:52:28

58

Views

Number of $2$-Sylow subgroups in $A_4 \times S_4$

Published on 18 Oct 2016 - 5:52

score 150 · Answer 11 · 2016-10-19 16:21:54

150

Views

Write the $p$-sylow subgroup as a quotient of the group.

Published on 19 Oct 2016 - 16:21

score 240 · Answer 12 · 2016-10-22 09:28:06

240

Views

Assume $p^2$ is not congruent to $1\mod q$ and that $q^2$ is not congruent to $1\mod p$. Classify all groups of order $p^2q^2$.

Published on 22 Oct 2016 - 9:28

score 298 · Answer 13 · 2016-10-24 01:04:06

298

Views

Suppose $p$ is prime and $G$ is a group and $|G| = p(p + 1)$. Prove $G$ has normal subgroup of order $p$ or a normal subgroup of order $p + 1$.

Published on 24 Oct 2016 - 1:04

score 280 · Answer 14 · 2016-10-24 21:27:26

280

Views

Prove no simple group of order 3675

Published on 24 Oct 2016 - 21:27

score 770 · Answer 15 · 2016-10-27 00:57:38

770

Views

Classify all groups of order 3825

Published on 27 Oct 2016 - 0:57

List Question

The Lemma for sylow theorem. show that prime $p$ divides $|X|-|X_G|$

Understanding the wreath product of $\mathbb Z_2$ by $\mathbb Z_2$ and of $\mathbb Z_2$ by $\mathbb Z_3$

$|G|=p(p+1)$ for $p$ prime, then $G$ has a normal subgroup of order $p$ or $p+1$

Why is it that every 2-Sylow subgroup of G is cyclic?

Cyclic groups of order $pq$ proof question

Show that $|K_{2,5}|=60.$

Proof explanation on a group of order $595$ having a normal Sylow $17$-subgroup.

Is my proof correct? Let $G$ be a group of order $10989$. Prove that $G$ contains either a normal Sylow $37$-subgroup or a normal Sylow $3$-subgroup

Proof of the first Sylow theorem in the Artin's textbook

Number of $2$-Sylow subgroups in $A_4 \times S_4$

Write the $p$-sylow subgroup as a quotient of the group.

Assume $p^2$ is not congruent to $1\mod q$ and that $q^2$ is not congruent to $1\mod p$. Classify all groups of order $p^2q^2$.

Suppose $p$ is prime and $G$ is a group and $|G| = p(p + 1)$. Prove $G$ has normal subgroup of order $p$ or a normal subgroup of order $p + 1$.

Prove no simple group of order 3675

Classify all groups of order 3825

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