Question

Quotient of finite, nilpotent group by Frattini subgroup is isomorphic to product of quotients of Sylow subgroups by their respective Frattini groups.

score 261 · Answer 1 · 2026-03-19 13:44:53

261

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Quotient of finite, nilpotent group by Frattini subgroup is isomorphic to product of quotients of Sylow subgroups by their respective Frattini groups.

Published on 19 Mar 2026 - 13:44

score 281 · Answer 2 · 2026-03-25 01:21:10

281

Views

Is the statement that $ \operatorname{Aut}( \operatorname{Hol}(Z_n)) \cong \operatorname{Hol}(Z_n)$ true for every odd $n$?

Published on 25 Mar 2026 - 1:21

score 90 · Answer 3 · 2026-03-26 20:40:44

90

Views

Finite groups isomorphic to a subgroup of $F^+$

Published on 26 Mar 2026 - 20:40

score 212 · Answer 4 · 2026-03-25 04:44:16

$G_1, G_2$ finite groups, for all primes $p$, Sylow $p$-subgroups of $G_1$ and $G_2$ are isomorpic and $|G_1|=|G_2|$ then $G_1 \cong G_2$.

score 106 · Answer 5 · 2026-03-25 04:44:20

106

Views

Let $G$ be finite and $P\lhd G$ $p$-sylow. For all $H<G$, $P\cap H$ is $p$-sylow of $H$.

Published on 25 Mar 2026 - 4:44

score 49 · Answer 6 · 2026-03-25 04:44:15

Let G be a finite group and N$\lhd$G such as p||N| (p dividing the order of N). Then for all P p-sylow subgroup of G, N$\cap$P$\ne{e}$

score 499 · Answer 7 · 2026-03-25 18:46:28

499

Views

Finite $p$-group with cyclic abelianization is abelian

Published on 25 Mar 2026 - 18:46

score 900 · Answer 8 · 2026-03-26 07:58:52

900

Views

How many group homomorphisms we can get from ${\mathbb Z}_{20}$ to ${\mathbb Z}_{10}$?

Published on 26 Mar 2026 - 7:58

score 384 · Answer 9 · 2026-03-25 04:41:21

384

Views

Flaw in my classification of groups of order 2015

Published on 25 Mar 2026 - 4:41

score 294 · Answer 10 · 2026-03-20 11:35:39

294

Views

Let G be $\mathbb Z_p\times\dots\times \mathbb Z_p$ . Find A(G).

Published on 20 Mar 2026 - 11:35

score 211 · Answer 11 · 2026-03-26 07:58:24

211

Views

Let $G=\Bbb Z_{30} \times \mathbb Z_{36}$.

Published on 26 Mar 2026 - 7:58

score 203 · Answer 12 · 2026-03-25 15:51:34

203

Views

Coloring the vertices of a decagon

Published on 25 Mar 2026 - 15:51

score 64 · Answer 13 · 2018-07-30 11:28:24

64

Views

If $P,Q$ are $p-$subgroup of $G$, then so is $PQ$.

Published on 30 Jul 2018 - 11:28

score 1.1k · Answer 14 · 2026-03-25 06:12:13

1.1k

Views

Putnam 2007 A5: Finite group $n$ elements order $p$, prove either $n=0$ or $p$ divides $n+1$

Published on 25 Mar 2026 - 6:12

score 857 · Answer 15 · 2018-07-31 05:31:43

857

Views

Example of a non-nilpotent finite group $G$ so that every non-trivial normal subgroup of $G$ intersects $Z(G)$ non-trivially?

Published on 31 Jul 2018 - 5:31

List Question

Quotient of finite, nilpotent group by Frattini subgroup is isomorphic to product of quotients of Sylow subgroups by their respective Frattini groups.

Is the statement that $ \operatorname{Aut}( \operatorname{Hol}(Z_n)) \cong \operatorname{Hol}(Z_n)$ true for every odd $n$?

Finite groups isomorphic to a subgroup of $F^+$

$G_1, G_2$ finite groups, for all primes $p$, Sylow $p$-subgroups of $G_1$ and $G_2$ are isomorpic and $|G_1|=|G_2|$ then $G_1 \cong G_2$.

Let $G$ be finite and $P\lhd G$ $p$-sylow. For all $H<G$, $P\cap H$ is $p$-sylow of $H$.

Let G be a finite group and N$\lhd$G such as p||N| (p dividing the order of N). Then for all P p-sylow subgroup of G, N$\cap$P$\ne{e}$

Finite $p$-group with cyclic abelianization is abelian

How many group homomorphisms we can get from ${\mathbb Z}_{20}$ to ${\mathbb Z}_{10}$?

Flaw in my classification of groups of order 2015

Let G be $\mathbb Z_p\times\dots\times \mathbb Z_p$ . Find A(G).

Let $G=\Bbb Z_{30} \times \mathbb Z_{36}$.

Coloring the vertices of a decagon

If $P,Q$ are $p-$subgroup of $G$, then so is $PQ$.

Putnam 2007 A5: Finite group $n$ elements order $p$, prove either $n=0$ or $p$ divides $n+1$

Example of a non-nilpotent finite group $G$ so that every non-trivial normal subgroup of $G$ intersects $Z(G)$ non-trivially?

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