# metacyclic group

## Definition

A metacyclic group is a group $G$ that possesses a normal subgroup $N$ such that $N$ and $G/N$ are both cyclic.

## Properties

Subgroups (http://planetmath.org/Subgroup) and quotients (http://planetmath.org/QuotientGroup) of metacyclic groups are also metacyclic.

Metacyclic groups are obviously supersolvable, with Hirsch length at most $2$.

Title metacyclic group MetacyclicGroup 2013-03-22 15:36:39 2013-03-22 15:36:39 yark (2760) yark (2760) 5 yark (2760) Definition msc 20F16 metacyclic