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...

the cyclic groups, the dicyclic groups, and the direct products of two cyclic groups. The polycyclic groups generalize metacyclic groups by allowing...

textbooks these groups have no special name, other than metacyclic groups, but that term is often used more generally today. See metacyclic group for more on...

generalized quaternion groups. Any group such that all Sylow subgroups are cyclic is called a Z-group, and in particular must be a metacyclic group: this means it...

groups: Supersolvable groups are always polycyclic, and hence solvable. Every finitely generated nilpotent group is supersolvable. Every metacyclic group...

1) and the quotient group Gi+1 / Gi is a cyclic group (for every i between 0 and n - 1) A metacyclic group is a polycyclic group with n ≤ 2, or in other...

radicals have a Galois group which is either the cyclic group of order 7, or the dihedral group of order 14 or a metacyclic group of order 21 or 42. The...

presentation. This group is a metacyclic group of order 4mn with abelianization of order 4m (so m and n are both determined by this group). The element y...

parasite passing its life cycle in two different hosts. In humans the metacyclic promastigotes are injected by sandfly through the skin during its blood...

Leishmania. The sandflies inject the infective stage, metacyclic promastigotes, during blood meals. Metacyclic promastigotes in the puncture wound are phagocytized...