If a group $G$ is infinite, prove that it has a non-trivial subgroup
46904
Let $G$ be a non-trivial group with no non-trivial proper subgroup. Prove that $G$ cannot be infinite group.
153921
Infinite nilpotent group, any normal subgroup intersects the center nontrivially
58033
$G\times H\cong G$ with $H$ non-trivial
75590
How many normal subgroups does a non-abelian group $G$ of order $ 21$
126113
Prove the existence of order 4 subgroups of order 8 groups
124709
Suppose G be a non-abelian group and H,K be two abelian subgroups of G. Then must HK be an abelian subgroup of G?
151130
When is the product of $n$ subgroups a subgroup?
156941
Subgroups of $\mathbb{Z}$
87534
Finitely generated group which is not finitely presented
79452
How to prove that it is a group?
88718
A group is generated by two elements of order $2$ is infinite and non-abelian
106277
Prove that $G$ contains a subgroup $H_i$ for each $i\in\Bbb Z$ with $\dots\subset H_{−2}\subset H_{−1}\subset H_0\subset H_1\subset\dots?$
116125
A group $G$ with $G'$ abelian and every abelian normal subgroup finite
3756
If $G$ is abelian, then the set of all $g \in G$ such that $g = g^{-1}$ is a subgroup of $G$
42582
Infinite group with only two conjugacy classes
29996
Prove that if a normal subgroup $H$ of $ G$ has index $n$, then $g^n \in H$ for all $g \in G$
121141
Proving Finiteness of Group from Presentation