Question

A presentation of group of order $p^3$ and exponent $p$

score 68 · Answer 1 · 2020-04-02 18:14:25

68

Views

A presentation of group of order $p^3$ and exponent $p$

Published on 02 Apr 2020 - 18:14

score 47 · Answer 2 · 2020-04-04 19:02:59

47

Views

Some results on derivation of a group

Published on 04 Apr 2020 - 19:02

score 81 · Answer 3 · 2020-04-05 22:11:51

81

Views

Proving $P$ is a Sylow $p$-group of $PN$

Published on 05 Apr 2020 - 22:11

score 91 · Answer 4 · 2020-04-15 02:59:48

91

Views

Semidirect product and group action

Published on 15 Apr 2020 - 2:59

score 65 · Answer 5 · 2020-04-20 16:37:47

65

Views

If $|G|=p^n$, then for any $H<G$, there is a $K\leq G$ such that $H\lhd K$ and $[K:H]=p$

Published on 20 Apr 2020 - 16:37

score 338 · Answer 6 · 2026-03-25 03:03:18

338

Views

Let $p$ be a prime number and let $G$ be a finite $p\text{-group}$. Let $M$ be a maximal subgroup of $G$.

Published on 25 Mar 2026 - 3:03

score 224 · Answer 7 · 2020-05-02 13:41:56

224

Views

How many subgroups does a Prüfer group have?

Published on 02 May 2020 - 13:41

score 183 · Answer 8 · 2020-05-11 21:41:29

183

Views

Group of order 81 and exponent 3

Published on 11 May 2020 - 21:41

score 954 · Answer 9 · 2020-05-23 10:27:39

Let $G$ be a p-group. Let $H$ be a proper subgroup of $G$. Show that there exists $g$ $\in$ $G \setminus H$ such that $gHg^{-1}=H$.

score 231 · Answer 10 · 2020-05-23 16:41:57

231

Views

A simple group with $|\operatorname{Syl}_p⁡ G| \le 6$ is cyclic

Published on 23 May 2020 - 16:41

score 107 · Answer 11 · 2020-05-26 13:59:54

107

Views

Group of order $q^3p^3$, where $p,q$ are twin primes greater than $10$, is solvable

Published on 26 May 2020 - 13:59

score 398 · Answer 12 · 2020-05-31 19:32:45

398

Views

The cyclic subgroups of $p^2$ order non-cyclic group are normal

Published on 31 May 2020 - 19:32

score 1k · Answer 13 · 2020-06-05 12:18:14

1k

Views

Let $G$ be a nonabelian group of order $p^{3},$ where $p$ is a prime. Show that $G$ has exactly $p^{2}+p-1$ distinct conjugacy classes.

Published on 05 Jun 2020 - 12:18

score 176 · Answer 14 · 2020-06-07 14:29:43

176

Views

How to find the number of elements of order $p$.

Published on 07 Jun 2020 - 14:29

score 209 · Answer 15 · 2020-06-13 10:41:59

209

Views

How to prove the number of the elements of order $p$ in a group of order $p^4$ is ${p^3}-1$

Published on 13 Jun 2020 - 10:41

List Question

A presentation of group of order $p^3$ and exponent $p$

Some results on derivation of a group

Proving $P$ is a Sylow $p$-group of $PN$

Semidirect product and group action

If $|G|=p^n$, then for any $H<G$, there is a $K\leq G$ such that $H\lhd K$ and $[K:H]=p$

Let $p$ be a prime number and let $G$ be a finite $p\text{-group}$. Let $M$ be a maximal subgroup of $G$.

How many subgroups does a Prüfer group have?

Group of order 81 and exponent 3

Let $G$ be a p-group. Let $H$ be a proper subgroup of $G$. Show that there exists $g$ $\in$ $G \setminus H$ such that $gHg^{-1}=H$.

A simple group with $|\operatorname{Syl}_p⁡ G| \le 6$ is cyclic

Group of order $q^3p^3$, where $p,q$ are twin primes greater than $10$, is solvable

The cyclic subgroups of $p^2$ order non-cyclic group are normal

Let $G$ be a nonabelian group of order $p^{3},$ where $p$ is a prime. Show that $G$ has exactly $p^{2}+p-1$ distinct conjugacy classes.

How to find the number of elements of order $p$.

How to prove the number of the elements of order $p$ in a group of order $p^4$ is ${p^3}-1$

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