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 KB (170 words) - 09:22, 20 September 2021
the cyclic groups, the dicyclic groups, and the direct products of two cyclic groups. The polycyclic groups generalize metacyclic groups by allowing...
36 KB (4,113 words) - 03:36, 18 July 2024
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...
7 KB (889 words) - 01:36, 13 November 2023
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...
9 KB (1,272 words) - 04:50, 12 August 2024
groups: Supersolvable groups are always polycyclic, and hence solvable. Every finitely generated nilpotent group is supersolvable. Every metacyclic group...
4 KB (491 words) - 03:55, 25 March 2024
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...
4 KB (539 words) - 17:45, 23 September 2022
Septic equation (section Galois groups)
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...
7 KB (911 words) - 07:11, 13 February 2024
Spherical 3-manifold (category Group theory)
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...
8 KB (1,378 words) - 21:27, 18 August 2024
parasite passing its life cycle in two different hosts. In humans the metacyclic promastigotes are injected by sandfly through the skin during its blood...
37 KB (4,436 words) - 02:24, 19 April 2024
Leishmania. The sandflies inject the infective stage, metacyclic promastigotes, during blood meals. Metacyclic promastigotes in the puncture wound are phagocytized...
50 KB (4,992 words) - 01:55, 19 October 2024