Finitep-groups with a cyclic commutator subgroup

1995 ◽  
Vol 34 (2) ◽  
pp. 125-129 ◽  
Author(s):  
A. A. Finogenov
Keyword(s):  
Commutator Subgroup ◽  
Cyclic Commutator

scholarly journals Local nearrings on finite non-abelian $2$-generated $p$-groups

2020 ◽  
Vol 12 (1) ◽  
pp. 199-207
Author(s):  
I.Yu. Raievska ◽  
M.Yu. Raievska
Keyword(s):  
Commutator Subgroup ◽  
Additive Group ◽  
Nilpotency Class ◽  
Invertible Elements ◽  
Cyclic Commutator

It is proved that for ${p>2}$ every finite non-metacyclic $2$-generated p-group of nilpotency class $2$ with cyclic commutator subgroup is the additive group of a local nearring and in particular of a nearring with identity. It is also shown that the subgroup of all non-invertible elements of this nearring is of index $p$ in its additive group.

A particular class of supersoluble groups

1994 ◽  
Vol 57 (3) ◽  
pp. 357-364 ◽  
Author(s):  
W. Dirscherl ◽  
H. Heineken
Keyword(s):  
Finite Groups ◽  
Quotient Group ◽  
Commutator Subgroup ◽  
Supersoluble Groups ◽  
Cyclic Commutator

AbstractWe consider (finite) groups in which every two-generator subgroup has cyclic commutator subgroup. Among other things, these groups are metabelian modulo their hypercentres, and in the corresponding quotient group all subgroups of the commutator subgroup are normal.

On finitep-groups with cyclic commutator subgroup

1982 ◽  
Vol 39 (4) ◽  
pp. 295-298 ◽  
Author(s):  
Ying Cheng
Keyword(s):  
Commutator Subgroup ◽  
Cyclic Commutator

scholarly journals Automorphism groups with cyclic commutator subgroup and Hamilton cycles

1998 ◽  
Vol 189 (1-3) ◽  
pp. 69-78 ◽  
Author(s):  
Edward Dobson ◽  
Heather Gavlas ◽  
Joy Morris ◽  
Dave Witte
Keyword(s):  
Commutator Subgroup ◽  
Automorphism Groups ◽  
Hamilton Cycles ◽  
Cyclic Commutator

On p-groups with a cyclic commutator subgroup

1975 ◽  
Vol 20 (2) ◽  
pp. 178-198 ◽  
Author(s):  
R. J. Miech
Keyword(s):  
Commutator Subgroup ◽  
Metabelian Group ◽  
Special Kind ◽  
Complete Classification ◽  
Isomorphism Problem ◽  
Point Of View ◽  
Defining Relations ◽  
Group A ◽  
Cyclic Commutator

This paper contains the complete classification of the finite p-groups G where p is an odd prime, G is generated by two elements, and the commutator subgroup of G is cyclic. These groups are a special kind of two-generator metabelian group, a class that has been studied by Szekeres (1965). He determined the defining relations of such groups but, as he noted, a “residual isomorphism problem” remains. The cyclic commutator groups are simple when considered from this first point of view; they have a short, easily derived set of defining relations. However, the isomorphism problem is a bit complicated for the defining relations contain nine parameters and each of these parameters might and can be an invariant of the group.

scholarly journals ON THE EXISTENCE OF NONINNER AUTOMORPHISMS OF ORDER TWO IN FINITE 2-GROUPS

2012 ◽  
Vol 87 (2) ◽  
pp. 278-287 ◽  
Author(s):  
A. R. JAMALI ◽  
M. VISEH
Keyword(s):  
Commutator Subgroup ◽  
Cyclic Commutator

AbstractIn this paper we prove that every nonabelian finite 2-group with a cyclic commutator subgroup has a noninner automorphism of order two fixing either Φ(G) or Z(G) elementwise. This, together with a result of Peter Schmid on regular p-groups, extends our result to the class of nonabelian finite p-groups with a cyclic commutator subgroup.

Finitep-groups with cyclic commutator subgroup and cyclic center

1998 ◽  
Vol 63 (6) ◽  
pp. 802-812
Author(s):  
A. A. Finogenov
Keyword(s):  
Commutator Subgroup ◽  
Cyclic Commutator
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