Does every infinite finitely generated group contains an element of infinite period?
6189
Examples of infinite groups such that all their respective elements are of finite order.
99782
$a_{n+1}=|a_n|-a_{n-1} \implies a_n \; \text{is periodic}$
142472
Every finite group has a composition series
54236
Does every Abelian group admit a ring structure?
158873
Is every group the unit group of some ring?
114187
In a finite cyclic group, the generator has the order of the group
117211
Infinite linear independent family in a finitely generated $A$-module
123677
Normal subgroups of infinite symmetric group
124472
Elements with infinite roots in $p$-adic integers
72991
Is every group the automorphism group of a group?
76504
Non-trivial cyclic group with unique generator
30825
Infinite coproduct of abelian groups
64193
Cardinality of Infinite Symmetric group
42582
Infinite group with only two conjugacy classes
57309
Show that the free group on $n$ generators is a finite index subgroup of $F_2$
81543
Finite abelian group contains an element with order equal to the lcm of the orders of its elements
53357
Cyclic Group Generators of Order $n$