Newbetuts

Show that the representation $\mathbb Z\ni a\mapsto\begin{pmatrix}1& a\\0&1\end{pmatrix}$ is not completely reducible

Finding Sylow 2-subgroups of the dihedral group $D_n$

Action via automorphism

Group tables for a group of four elements.

How many groups of order at most $25$ are "pleasant" (abelian, with every non-identity element having prime order)?

Identity element in a finite cyclic group $G$.

Prove that the augmentation ideal in the group ring $\mathbb{Z}/p\mathbb{Z}G$ is a nilpotent ideal ($p$ is a prime, $G$ is a $p$-group)

Let $f: (\Bbb Z_{28}, +)\to(\Bbb Z_{16}, +)$ be a group homomorphism such that $f(1)=12$. Find $\ker f$.

If $|G|=p^3q^2$ then $\Phi(G)$ is cyclic for primes $p\neq q$.

"Tensor complement" of representations of finite groups

Derived subgroups of $SL(2,2)$, $SL(2,3)$ and $GL(2,3)$

Show that $PSL(3,4)$ has no element of order $15$.

Structure of simple group of order 168 just via Sylow theory (fix for Math Doctor Bob)

An irreducible representation of a finite group whose symmetric square is also irreducible

Schur–Zassenhaus exercise: coprime subgroup contained in a complement

Is there a counterexample to this weakened converse of Hall's theorem?

New posts in finite-groups

An abelian group of order 100

Prove that $H$ is a abelian subgroup of odd order

Show that there is a positive integer $n$ such that $G \cong \ker(\phi^{n}) \times \phi^{n}(G)$

Prove that a non-abelian group of order $pq$ ($p<q$) has a nonnormal subgroup of index $q$

Show that the representation $\mathbb Z\ni a\mapsto\begin{pmatrix}1& a\\0&1\end{pmatrix}$ is not completely reducible

Finding Sylow 2-subgroups of the dihedral group $D_n$

Action via automorphism

Group tables for a group of four elements.

How many groups of order at most $25$ are "pleasant" (abelian, with every non-identity element having prime order)?

Identity element in a finite cyclic group $G$.

Prove that the augmentation ideal in the group ring $\mathbb{Z}/p\mathbb{Z}G$ is a nilpotent ideal ($p$ is a prime, $G$ is a $p$-group)

Let $f: (\Bbb Z_{28}, +)\to(\Bbb Z_{16}, +)$ be a group homomorphism such that $f(1)=12$. Find $\ker f$.

If $|G|=p^3q^2$ then $\Phi(G)$ is cyclic for primes $p\neq q$.

"Tensor complement" of representations of finite groups

Derived subgroups of $SL(2,2)$, $SL(2,3)$ and $GL(2,3)$

Show that $PSL(3,4)$ has no element of order $15$.

Structure of simple group of order 168 just via Sylow theory (fix for Math Doctor Bob)

An irreducible representation of a finite group whose symmetric square is also irreducible

Schur–Zassenhaus exercise: coprime subgroup contained in a complement

Is there a counterexample to this weakened converse of Hall's theorem?