Is $G$ a group under those conditions?
17997
Right identity and Right inverse implies a group
30676
$G'$ and the product of all the elements in an odd order group
133001
$G$ simple group and there exists a subgroup of index $n$. Show that: $|G|$ divides $n!/2$
102622
K is a subgroup of G. Show that K is not a normal subgroup
21673
If $|G| = p^n$ then $G$ has a subgroup of order $p^m$ for all $0\le m <n.$
59128
If $|\lbrace g \in G: \pi (g)=g^{-1} \rbrace|>\frac{3|G|}{4}$, then $G$ is an abelian group.
44152
If $G$ has only one subgroup of order $n$, then that Subgroup is Normal
98739
If $H$ is a subgroup of $G$ and $K$ is a subgroup of $H$, then $$|G:K|=|G:H||H:K|$$
43651
Normal subgroups and factor groups
106779
How to show if $H,K$ are normal subgroups in a group $G$ then $[H,K] \leq H \cap K$
132704
If G is not commutative, then is there always a subgroup that is not a normal subgroup?
103216
The set $\{g^2 | g \in G\}$ in a group $G$
146952
When can I say that $\cup H_i$ is a group?
95534
If $|G|=p^nq$, then $G$ contains a unique normal subgroup of index $q$
46904
Let $G$ be a non-trivial group with no non-trivial proper subgroup. Prove that $G$ cannot be infinite group.
15633
If G is a group of even order, prove it has an element $a \neq e$ satisfying $a^2 = e$.
11957
G is the product of its Sylow subgroups