Rephrase the proof "For all odd n, there exists a Group G ..."
92057
Prove that for every odd integer n, there is a group...
135701
An example of a group such that $G \cong G \times G$
25404
Let $G$ be a group of order $2m$ where $m$ is odd. Prove that $G$ contains a normal subgroup of order $m$
150199
How to prove for a finite group that $|\langle g \rangle|=o(g)$?
15633
If G is a group of even order, prove it has an element $a \neq e$ satisfying $a^2 = e$.
67554
In a group, the number of non-self-inverse elements is even
149216
Give a combinatorial proof to show the following for all integers $n \geq 2$.
70394
Prove that $a * b$ is a group (Hungerford, 2nd ed., sec $7.2$, Exercise $22$)
104349
Proof by induction involving symmetric groups
98474
Show the existence of a certain subgroup of F2
156641
Show that $\gcd(3n,3n+ 2) = 1$ when $n$ is odd
126113
Prove the existence of order 4 subgroups of order 8 groups
99630
For every $g\in G$ there exists an $h\in G$ such that $g = h^3$
139835
Every Finite Group is Isomorphic to a Subgroup of $A_n$
138601
There are $2n+1$ people. For each $n$ people there is somebody who is friend with each of them. Prove there is a "know-them-all" person.
102859
Proving that $G$ is a group if $a*x=b$ and $y*a=b$ have solutions.
110708
On proving that a finitely generated group has a finite number of subgroups with index $n$.