Give an example of a nonabelian group in which a product of elements of finite order can have infinite order.
58688
Example of a group where $o(a)$ and $o(b)$ are finite but $o(ab)$ is infinite
71035
Non abelian subgroup of a abelian group.
59811
Finite Abelian groups with the same number of elements for all orders are isomorphic
145406
Prove every element of $G$ has finite order.
101735
A finite $p$-group cannot be simple unless it has order $p$
62977
Show on $\mathbb{N}$ there are $2^{\aleph_0}$ nonisomorphic linear orders.
61546
Prove that for each prime $p$ there exists a nonabelian group of order $p^3$
114187
In a finite cyclic group, the generator has the order of the group
116080
Let G be a finite group with more than one element. Show that G has an element of prime order
150961
An example for a homomorphism that is not an automorphism
145127
For any integers $m,n>1$ , does there exist a group $G$ with elements $a,b \in G$ such that $o(a)=m , o(b)=n$ but $ab$ has infinite order ?
67554
In a group, the number of non-self-inverse elements is even
121810
Prove that the product of two infinite cyclic groups is not infinite cyclic.
83654
Order of an element in a finite cyclic group
98436
Finite order endomorphisms
42582
Infinite group with only two conjugacy classes
139611
Can a normal subgroup of a finite nonabelian group be nonabelian?