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New posts in finite-groups
Subrings of finite index and units
group-theory
ring-theory
finite-groups
Writing a group element as $ghg^{-1} h^{-1}$ and as $g^2 h^2$
abstract-algebra
group-theory
finite-groups
representation-theory
alternative-proof
$|G| + \frac{|G|}{\left|\langle a\rangle\right|} + \frac{|G|}{\left|\langle b\rangle\right|} + \frac{|G|}{\left|\langle ab\rangle\right|}$
abstract-algebra
group-theory
finite-groups
At most one subgroup of every order dividing $\lvert G\rvert$ implies $G$ cyclic [closed]
abstract-algebra
group-theory
finite-groups
cyclic-groups
Groups of order $p^3$
abstract-algebra
group-theory
finite-groups
groups-enumeration
For $p,q$ primes such that $q|p-1$, show there is only one non-abelian group of order $pq$, up to isomorphism
group-theory
finite-groups
Is a finite group generated by representatives of its conjugacy classes?
group-theory
finite-groups
Are there any distinct finite simple groups with the same order?
group-theory
finite-groups
simple-groups
Generalization of index 2 subgroups are normal
abstract-algebra
group-theory
finite-groups
symmetric-groups
Pontryagin duality for finite groups
abstract-algebra
group-theory
finite-groups
duality-theorems
Irreducible representations (over $\mathbb{C}$) of dihedral groups
group-theory
finite-groups
representation-theory
Existence of normal subgroups for a group of order $36$
abstract-algebra
finite-groups
Prove Fitting's theorem for finite groups
group-theory
finite-groups
normal-subgroups
nilpotent-groups
Putnam 2007 A5: Finite group $n$ elements order $p$, prove either $n=0$ or $p$ divides $n+1$
abstract-algebra
group-theory
finite-groups
contest-math
sylow-theory
How many different groups of order $15$ there are?
abstract-algebra
group-theory
finite-groups
groups-enumeration
$G$ is characteristically simple $\iff$ there is simple $T$ such that $G \cong T\times T \times \cdots \times T$
group-theory
finite-groups
simple-groups
characteristic-subgroups
Group $G$ of order $p^2$: $\;G\cong \mathbb Z_{p^2}$ or $G\cong \mathbb Z_p \times \mathbb Z_p$ [closed]
abstract-algebra
group-theory
finite-groups
No homomorphism from $Z_{16}\oplus Z_{2}$ onto $Z_{4}\oplus Z_{4}$.
abstract-algebra
group-theory
finite-groups
group-isomorphism
group-homomorphism
Prove: $D_{8n} \not\cong D_{4n} \times Z_2$.
abstract-algebra
group-theory
finite-groups
dihedral-groups
Finitely generated torsion abelian group
abstract-algebra
group-theory
proof-verification
finite-groups
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