New posts in Infinite Groups

Number of elements of order $p$ in a (possibly infinite) group

Are there any finite examples of metachirality?

The order of elements in infinite quotient groups

Are these infinite groups decomposable?

Every infinite group has a non-trivial subgroup

Isomorphic subgroups such that the quotient is isomorphic.

Can the group $\mathbb Z \times \mathbb Z$ be written as union of finitely many proper subgroups of it?

The number of elements not in conjugate of a subgroup

Is there a group $G$ and subgroup $H$, such that there exists $g\in G$ with $gHg^{-1} \subset H$ and $|H:gHg^{-1}|$ is infinite?

Can an uncountable group have a countable number of subgroups?