Newbetuts

can one order the elements of a finite group such that their product is equal to the first element in the list?

How many non isomorphic groups of order 30 are there?

For a group $G$ of order $p^n$, $G\cong H$ for some $H\le\Bbb Z_p\wr\dots\wr\Bbb Z_p$.

Permutation of cosets

When is $\mathfrak{S}_n \times \mathfrak{S}_m$ a subgroup of $\mathfrak{S}_p$?

Finite abelian $p$-group with only one subgroup size $p$ is cyclic

$A_6 \simeq \mathrm{PSL}_2(\mathbb{F}_9) $ only simple group of order 360

No group of order 400 is simple

What finite groups always have a square root for each element?

Finding the automorphisms of $S_3$ by looking at the orders of the elements

On Groups of Order 315 with a unique sylow 3-subgroup .

Abelian $p$-group with unique subgroup of index $p$

Finite abelian groups - direct sum of cyclic subgroup

If H is a subgroup of G, then H has no more Sylow subgroups than G

If $G$ has only 2 proper, non-trivial subgroups then $G$ is cyclic

If $H$ is a proper subgroup of a $p$-group $G$, then $H$ is proper in $N_G(H)$.

Any subgroup of index $p$ in a $p$-group is normal.

New posts in finite-groups

Finding the number of elements of order two in the symmetric group $S_4$

For which $n$, $G$ is abelian?

$G$ is a group of odd order, show that $a^2=b^2 \Rightarrow a=b$

can one order the elements of a finite group such that their product is equal to the first element in the list?

How many non isomorphic groups of order 30 are there?

For a group $G$ of order $p^n$, $G\cong H$ for some $H\le\Bbb Z_p\wr\dots\wr\Bbb Z_p$.

Permutation of cosets

When is $\mathfrak{S}_n \times \mathfrak{S}_m$ a subgroup of $\mathfrak{S}_p$?

Finite abelian $p$-group with only one subgroup size $p$ is cyclic

$A_6 \simeq \mathrm{PSL}_2(\mathbb{F}_9) $ only simple group of order 360

No group of order 400 is simple

What finite groups always have a square root for each element?

Finding the automorphisms of $S_3$ by looking at the orders of the elements

On Groups of Order 315 with a unique sylow 3-subgroup .

Abelian $p$-group with unique subgroup of index $p$

Finite abelian groups - direct sum of cyclic subgroup

If H is a subgroup of G, then H has no more Sylow subgroups than G

If $G$ has only 2 proper, non-trivial subgroups then $G$ is cyclic

If $H$ is a proper subgroup of a $p$-group $G$, then $H$ is proper in $N_G(H)$.

Any subgroup of index $p$ in a $p$-group is normal.