New posts in finite-groups

Subrings of finite index and units

Writing a group element as $ghg^{-1} h^{-1}$ and as $g^2 h^2$

$|G| + \frac{|G|}{\left|\langle a\rangle\right|} + \frac{|G|}{\left|\langle b\rangle\right|} + \frac{|G|}{\left|\langle ab\rangle\right|}$

At most one subgroup of every order dividing $\lvert G\rvert$ implies $G$ cyclic [closed]

Groups of order $p^3$

For $p,q$ primes such that $q|p-1$, show there is only one non-abelian group of order $pq$, up to isomorphism

Is a finite group generated by representatives of its conjugacy classes?

Are there any distinct finite simple groups with the same order?

Generalization of index 2 subgroups are normal

Pontryagin duality for finite groups

Irreducible representations (over $\mathbb{C}$) of dihedral groups

Existence of normal subgroups for a group of order $36$

Prove Fitting's theorem for finite groups

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

How many different groups of order $15$ there are?

$G$ is characteristically simple $\iff$ there is simple $T$ such that $G \cong T\times T \times \cdots \times T$

Group $G$ of order $p^2$: $\;G\cong \mathbb Z_{p^2}$ or $G\cong \mathbb Z_p \times \mathbb Z_p$ [closed]

No homomorphism from $Z_{16}\oplus Z_{2}$ onto $Z_{4}\oplus Z_{4}$.

Prove: $D_{8n} \not\cong D_{4n} \times Z_2$.

Finitely generated torsion abelian group