Newbetuts

Let $G$ be a group, and let $n\in\mathbb Z$. Show that $(ab)^n=a^nb^n\iff(ab)^{1-n}=a^{1-n}b^{1-n}$.

Why is $PGL_2(5)\cong S_5$?

Why is the number of subgroups of a finite group G of order a fixed p-power congruent to 1 modulo p?

Techniques for showing that a subgroup is not normal

Am I computing the centralizer of $(1, 2, 3)$ in $A_4$ correctly?

Generating lookup tables for Thistlethwaite's algorithm

A group of order $30$ has a normal $5$-Sylow subgroup.

Is it true, that for any two non-isomorphic finite groups $G$ and $H$ there exists such a group word $w$, that $|V_w(G)| \neq |V_w(H)|$?

Group theory conjectures

Every nonabelian group of order 6 has a non-normal subgroup of order 2 (revisited)

Which finite groups have their minimal permutation degree equal to their order?

Torsion in free products of groups

About the Center of the Special Linear Group $SL(n,F)$

Automorphism group of a topological space

Proof of Zassenhaus Lemma

New posts in group-theory

Can you always find a surjective endomorphism of groups such that it is not injective?

Proof that $U(n)$ is connected

A representation of a finite group which is not completely reducible

Profinite topology of a Group

Groups of order $pq$ have a proper normal subgroup

Let $G$ be a group, and let $n\in\mathbb Z$. Show that $(ab)^n=a^nb^n\iff(ab)^{1-n}=a^{1-n}b^{1-n}$.

Why is $PGL_2(5)\cong S_5$?

Why is the number of subgroups of a finite group G of order a fixed p-power congruent to 1 modulo p?

Techniques for showing that a subgroup is not normal

Am I computing the centralizer of $(1, 2, 3)$ in $A_4$ correctly?

Generating lookup tables for Thistlethwaite's algorithm

A group of order $30$ has a normal $5$-Sylow subgroup.

Is it true, that for any two non-isomorphic finite groups $G$ and $H$ there exists such a group word $w$, that $|V_w(G)| \neq |V_w(H)|$?

Group theory conjectures

Every nonabelian group of order 6 has a non-normal subgroup of order 2 (revisited)

Which finite groups have their minimal permutation degree equal to their order?

Torsion in free products of groups

About the Center of the Special Linear Group $SL(n,F)$

Automorphism group of a topological space

Proof of Zassenhaus Lemma