If $G$ is a finite group then ...
112872
Involutions and Abelian Groups
130937
Embeddings of finite groups into $\mathrm{GL}_n(\mathbb{Z})$
142228
Proof that a subset closed under group operation of a finite group is a subgroup
15633
If G is a group of even order, prove it has an element $a \neq e$ satisfying $a^2 = e$.
5297
If G is a finite abelian group and $a_1,...,a_n$ are all its elements, show that $x=a_1a_2a_3...a_n$must satisfy $x^2=e$.
40846
When can a (finite) group be written as the quotient of some other group by its center?
133770
Subgroups of finite abelian groups.
102971
Product of all elements of a finite group with an unique element of order 2
49768
If Gal(K,Q) is abelian then |Gal(K,Q)|=n
52121
Let $G$ be a finite group with $|G|>2$. Prove that ${\rm Aut}(G)$ contains at least two elements.
112993
Is every quotient of a finite abelian group $G$ isomorphic to some subgroup of $G$?
121077
Product of all elements in finite group
57464
If $G$ is a group show that if $(a \cdot b)^2 = a^2 \cdot b^2$ then $G$ must be abelian.
15526
Question on groups of order $pq$
3756
If $G$ is abelian, then the set of all $g \in G$ such that $g = g^{-1}$ is a subgroup of $G$
143451
Homomorphism from $(\Bbb Q,+)$ to a finite group
145563
In an abelian group, the elements of finite order form a subgroup.