Let $G$ be a group containing exactly $2n$ elements, $n\ge1$ integer.
26398
Group of even order contains an element of order 2
5692
Proving that there is a perfect square between $n$ and $2n$
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 $x^2=e$.
88718
A group is generated by two elements of order $2$ is infinite and non-abelian
5089
An element of a group has the same order as its inverse
135701
An example of a group such that $G \cong G \times G$
109053
Show that a finite cyclic group of order $n$ has exactly one subgroup of order $d$ dividing $n$ and these are all the subgroups it has
81864
Finite group of order $mn$ with $\gcd(m,n) = 1$ .
49768
If Gal(K,Q) is abelian then |Gal(K,Q)|=n
59561
Suppose that G is a group and N < G a normal subgroup. Prove G/N is simple
150199
How to prove for a finite group that $|\langle g \rangle|=o(g)$?
104855
Prove that $N \subset Z(G)$
11003
Proving that $G/N$ is an abelian group
101345
Suppose $n$ is an even positive integer and $H$ is a subgroup of $\mathbb Z/n \mathbb Z$. Prove that either every element of $H$ is...
30676
$G'$ and the product of all the elements in an odd order group
53409
Show group of order $4n + 2$ has a subgroup of index 2.
81543
Finite abelian group contains an element with order equal to the lcm of the orders of its elements