Existence of elementd of infinite order in finitely generated infinite group
126426
Does every infinite finitely generated group contains an element of infinite period?
3104
Prove that a group is infinite and nonabelian.
82009
Prove that every totally ordered set has a well-ordered cofinal subset
121481
Non-abelian finite $p$-group in which every element has prime order?
92750
Groups where all elements are order 3
116955
Showing the existence of a certain kind of extension of a finitely generated algebra
66398
Union of a finite set and a countably infinite set is countably infinite
149673
Cardinality of an infinite union of finite sets
128692
Example of an infinite group where every element except identity has order 2
84789
Order of products of elements in a finite Abelian group
157806
Order of a element on a Symmetric Group
157841
Existence of a non-abelian group of order $p^n$.
86926
Why isn't this a well ordering of $\{A\subseteq\mathbb N\mid A\text{ is infinite}\}$?
89508
Existence of normal subgroups for a group of order $36$
152604
For a finite group of order $2n$ does there exist $x$ such that $x\ast x=e$?
60075
Does there exist an $n$ such that all groups of order $n$ are Abelian?
138768
Showing that the family of Borel sets is countably generated