Metacyclic group

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In group theory, a metacyclic group is an extension of a cyclic group by a cyclic group. That is, it is a group G for which there is a short exact sequence

1 \rightarrow K \rightarrow G \rightarrow H \rightarrow 1,\,

where H and K are cyclic. Equivalently, a metacyclic group is a group G having a cyclic normal subgroup N, such that the quotient G/N is also cyclic.

Properties[edit]

Metacyclic groups are both supersolvable and metabelian.

Examples[edit]

References[edit]