Metacyclic Groups and the D(2) Problem

10.1142/11897 ◽  
2021 ◽  
Author(s):  
Francis E A Johnson
Keyword(s):  
Metacyclic Groups

scholarly journals Strong duality for metacyclic groups

2002 ◽  
Vol 73 (3) ◽  
pp. 377-392 ◽  
Author(s):  
R. Quackenbush ◽  
C. S. Szabó
Keyword(s):  
Finite Group ◽  
Dihedral Group ◽  
Strong Duality ◽  
Sylow Subgroups ◽  
Metacyclic Groups ◽  
Group D

AbstractDavey and Quackenbush proved a strong duality for each dihedral group Dm with m odd. In this paper we extend this to a strong duality for each finite group with cyclic Sylow subgroups (such groups are known to be metacyclic).

scholarly journals Locally Primitive Normal Cayley Graphs of Metacyclic Groups

10.37236/185 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
Jiangmin Pan
Keyword(s):  
Dihedral Group ◽  
Cayley Graphs ◽  
Complete Characterization ◽  
Metacyclic Group ◽  
Metacyclic Groups ◽  
Normal Cayley Graphs

A complete characterization of locally primitive normal Cayley graphs of metacyclic groups is given. Namely, let $\Gamma={\rm Cay}(G,S)$ be such a graph, where $G\cong{\Bbb Z}_m.{\Bbb Z}_n$ is a metacyclic group and $m=p_1^{r_1}p_2^{r_2}\cdots p_t^{r_t}$ such that $p_1 < p_2 < \dots < p_t$. It is proved that $G\cong D_{2m}$ is a dihedral group, and $val(\Gamma)=p$ is a prime such that $p|(p_1(p_1-1),p_2-1,\dots,p_t-1)$. Moreover, three types of graphs are constructed which exactly form the class of locally primitive normal Cayley graphs of metacyclic groups.

Finite metacyclic groups all extensions of which split

1978 ◽  
Vol 79 (3-4) ◽  
pp. 285-291 ◽  
Author(s):  
John S. Rose
Keyword(s):  
Metacyclic Groups

SynopsisThe groups of the title are characterized arithmetically.

Metacyclic groups

2000 ◽  
Vol 28 (8) ◽  
pp. 3865-3897 ◽  
Author(s):  
C.E. Hempel
Keyword(s):  
Metacyclic Groups

scholarly journals Commutation semigroups of finite metacyclic groups with trivial centre

2020 ◽  
Vol 100 (3) ◽  
pp. 765-789
Author(s):  
Darien DeWolf ◽  
Charles C. Edmunds
Keyword(s):  
Metacyclic Groups ◽  
Trivial Centre
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