scholarly journals Character tables of p-groups with derived subgroup of prime order III

2009 ◽  
Vol 321 (4) ◽  
pp. 1168-1195 ◽  
Author(s):  
Adriana Nenciu
Keyword(s):  
Prime Order ◽  
Character Tables ◽  
Derived Subgroup

scholarly journals A characterisation of cyclic subnormal separated A-groups of nilpotent length three

1997 ◽  
Vol 56 (2) ◽  
pp. 243-251
Author(s):  
Muhammad Umar Makarfi
Keyword(s):  
Prime Order ◽  
Separation Condition ◽  
Fitting Subgroup ◽  
Nilpotent Length ◽  
Monolithic Group ◽  
Derived Subgroup ◽  
Trivial Centre ◽  
Image Position

The paper gives a detailed description of all those finite A-groups of nilpotent length three that satisfy the cyclic subnormal separation condition. It is shown that every monolithic group under discussion is an extension of its Fitting subgroup P, which is a homocyclic p-group, by a p′ metabelian subgroup H, where p is a prime. The centraliser of P in H is trivial while the monolith W is equal to ω1(P) and the action of H on W is faithful and irreducible. H is further shown to have non trivial centre and is an extension of its derived subgroup M by a subgroup L such thatfor all primes q where Mq and Lq are the respective Sylow q-subgroups of M and L. The Fitting subgroup of F of H is shown to be M × Z(H), while Z(H) = F ∩ L and every element of L of prime order is in Z(H). Finally it is shown that if ql(q) is the exponent of Mq then every element of order dividing ql(q) in L belongs to Z(H).

Functional encryption for computational hiding in prime order groups via pair encodings

2017 ◽  
Vol 86 (1) ◽  
pp. 97-120 ◽  
Author(s):  
Jongkil Kim ◽  
Willy Susilo ◽  
Fuchun Guo ◽  
Man Ho Au
Keyword(s):  
Prime Order ◽  
Functional Encryption

Fusions of character tables III: Fusions of cyclic groups and a generalisation of a condition of Camina

2010 ◽  
Vol 178 (1) ◽  
pp. 325-348 ◽  
Author(s):  
Stephen P. Humphries ◽  
Brent L. Kerby ◽  
Kenneth W. Johnson
Keyword(s):  
Cyclic Groups ◽  
Character Tables

Finite groups with two supersoluble subgroups

2019 ◽  
Vol 22 (2) ◽  
pp. 297-312 ◽  
Author(s):  
Victor S. Monakhov ◽  
Alexander A. Trofimuk
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Sufficient Conditions ◽  
Maximal Subgroups ◽  
Sylow Subgroups ◽  
Derived Subgroup ◽  
Nilpotent Residual ◽  
A Finite Group

AbstractLetGbe a finite group. In this paper we obtain some sufficient conditions for the supersolubility ofGwith two supersoluble non-conjugate subgroupsHandKof prime index, not necessarily distinct. It is established that the supersoluble residual of such a group coincides with the nilpotent residual of the derived subgroup. We prove thatGis supersoluble in the following cases: one of the subgroupsHorKis nilpotent; the derived subgroup{G^{\prime}}ofGis nilpotent;{|G:H|=q>r=|G:K|}andHis normal inG. Also the supersolubility ofGwith two non-conjugate maximal subgroupsMandVis obtained in the following cases: all Sylow subgroups ofMand ofVare seminormal inG; all maximal subgroups ofMand ofVare seminormal inG.

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