Search results for "Central series"

Sylow numbers and nilpotent Hall subgroups

2013

Abstract Let π be a set of primes and G a finite group. We characterize the existence of a nilpotent Hall π-subgroup of G in terms of the number of Sylow subgroups for the primes in π.

A Characterization of the Class of Finite Groups with Nilpotent Derived Subgroup

2002

The class of all finite groups with nilpotent commutator subgroup is characterized as the largest subgroup-closed saturated formation 𝔉 for which the 𝔉-residual of a group generated by two 𝔉-subnormal subgroups is the subgroup generated by their 𝔉–residuals.

On Finite Solvable Groups That Behave Like Nilpotent Groups with Respect to the Frattini Group

1994

A note on strongly Lie nilpotency

1991

In this note the authors studies strongly Lie nilpotent rings and proves that if a ringR is strongly Lie nilpotent thenR(2), the ideal generated by all commutators, is nilpotent.

On finite products of nilpotent groups

1994

On the product of a nilpotent group and a group with non-trivial center

2007

Abstract It is proved that a finite group G = A B which is a product of a nilpotent subgroup A and a subgroup B with non-trivial center contains a non-trivial abelian normal subgroup.

On a theorem of Berkovich

2002

In a recent paper, Berkovich studied how to describe the nilpotent residual of a group in terms of the nilpotent residuals of some of its subgroups. That study required the knowledge of the structure of the minimal nonnilpotent groups, also called Schmidt groups. The major aim of this paper is to show that this description could be obtained as a consequence of a more complete property, giving birth to some interesting generalizations. This purpose naturally led us to the study of a family of subgroup-closed saturated formations of nilpotent type. An innovative approach to these classes is provided.

Nilpotent and perfect groups with the same set of character degrees

2014

We find a pair of finite groups, one nilpotent and the other perfect, with the same set of character degrees.

The Fitting Subgroup and Some Injectors of Radical Locally Finite Groups with min-pfor Allp

2003

Abstract This work was intended as an attempt to continue the study of the class ℬ of generalised nilpotent groups started in a previous paper. We present some results concerning the Fitting subgroup and the ℬ-injectors of a radical locally finite group satisfying min-p for all p.

Nilpotent Lie algebras with 2-dimensional commutator ideals

2011

Abstract We classify all (finitely dimensional) nilpotent Lie k -algebras h with 2-dimensional commutator ideals h ′ , extending a known result to the case where h ′ is non-central and k is an arbitrary field. It turns out that, while the structure of h depends on the field k if h ′ is central, it is independent of k if h ′ is non-central and is uniquely determined by the dimension of h . In the case where k is algebraically or real closed, we also list all nilpotent Lie k -algebras h with 2-dimensional central commutator ideals h ′ and dim k h ⩽ 11 .