Groups Saturated with Finite Frobenius Groups

2021 ◽  
Vol 109 (1-2) ◽  
pp. 270-279
Author(s):  
A. I. Sozutov
Keyword(s):  
Frobenius Groups

scholarly journals Tetravalent edge-transitive Cayley graphs of Frobenius groups

2021 ◽  
Vol 53 (2) ◽  
pp. 527-551
Author(s):  
Lei Wang ◽  
Yin Liu ◽  
Yanxiong Yan
Keyword(s):  
Cayley Graphs ◽  
Frobenius Groups ◽  
Edge Transitive

scholarly journals Frobenius groups of low rank

2021 ◽  
Author(s):  
Wolfgang Knapp ◽  
Peter Schmid
Keyword(s):  
Frobenius Group ◽  
Low Rank ◽  
Special Situation ◽  
Frobenius Groups ◽  
Frobenius Kernel

AbstractLet G be a finite Frobenius group of degree n. We show, by elementary means, that n is a power of some prime p provided the rank $${\mathrm{rk}}(G)\le 3+\sqrt{n+1}$$ rk ( G ) ≤ 3 + n + 1 . Then the Frobenius kernel of G agrees with the (unique) Sylow p-subgroup of G. So our result implies the celebrated theorems of Frobenius and Thompson in a special situation.

scholarly journals Cubic arc-transitive Cayley graphs on Frobenius groups

2018 ◽  
Vol 17 (07) ◽  
pp. 1850126 ◽  
Author(s):  
Hailin Liu ◽  
Lei Wang
Keyword(s):  
Automorphism Group ◽  
Cayley Graph ◽  
Cayley Graphs ◽  
Frobenius Groups

A Cayley graph [Formula: see text] is called arc-transitive if its automorphism group [Formula: see text] is transitive on the set of arcs in [Formula: see text]. In this paper, we give a characterization of cubic arc-transitive Cayley graphs on a class of Frobenius groups.

Camina Triples

2014 ◽  
Vol 57 (1) ◽  
pp. 125-131 ◽  
Author(s):  
Nabil M. Mlaiki
Keyword(s):  
Frobenius Groups

AbstractIn this paper, we study Camina triples. Camina triples are a generalization of Camina pairs, first introduced in 1978 by A. R. Camina. Camina’s work was inspired by the study of Frobenius groups. We show that if (G, N, M) is a Camina triple, then either G/N is a p-group, or M is abelian, or M has a non-trivial nilpotent or Frobenius quotient.

Transversal designs associated with frobenius groups

1981 ◽  
Vol 17 (1) ◽  
pp. 140-154 ◽  
Author(s):  
Dieter Jungnickel
Keyword(s):  
Frobenius Groups ◽  
Transversal Designs

scholarly journals Pentavalent arc-transitive Cayley graphs on Frobenius groups with soluble vertex stabilizer

2019 ◽  
Vol 17 (1) ◽  
pp. 513-518
Author(s):  
Hailin Liu
Keyword(s):  
Automorphism Group ◽  
Cayley Graph ◽  
Cayley Graphs ◽  
Frobenius Groups ◽  
Full Automorphism Group

Abstract A Cayley graph Γ is said to be arc-transitive if its full automorphism group AutΓ is transitive on the arc set of Γ. In this paper we give a characterization of pentavalent arc-transitive Cayley graphs on a class of Frobenius groups with soluble vertex stabilizer.

scholarly journals Supersolvable Frobenius groups with nilpotent centralizers

2019 ◽  
Vol 223 (3) ◽  
pp. 1210-1216
Author(s):  
Jhone Caldeira ◽  
Emerson de Melo
Keyword(s):  
Frobenius Groups
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