Finite Groups Whose Minimal Subgroups are Normal.
Finite groups whose poset of conjugacy classes of subgroups is isomorphic to the one of an abelian group
Si determinano i gruppi finiti il cui insieme parzialmente ordinato delle classi di coniugio dei sottogruppi è isomorfo a quello di un gruppo abeliano.
Finite groups whose set of numbers of subgroups of possible order has exactly 2 elements
Counting subgroups of finite groups is one of the most important topics in finite group theory. We classify the finite non-nilpotent groups whose set of numbers of subgroups of possible orders has exactly two elements. We show that if is a non-nilpotent group whose set of numbers of subgroups of possible orders has exactly 2 elements, then has a normal Sylow subgroup of prime order and is solvable. Moreover, as an application we give a detailed description of non-nilpotent groups with...
Finite groups with a standard component of type , - I
Finite groups with a standard-component of type , II
Finite groups with a unique nonlinear nonfaithful irreducible character
In this paper, we consider finite groups with precisely one nonlinear nonfaithful irreducible character. We show that the groups of order 16 with nilpotency class 3 are the only -groups with this property. Moreover we completely characterize the nilpotent groups with this property. Also we show that if is a group with a nontrivial center which possesses precisely one nonlinear nonfaithful irreducible character then is solvable.
Finite groups with an automorphism of prime order whose fixed points are in the Frattini of a nilpotent subgroup
In this paper it is proved that a finite group G with an automorphism of prime order r, such that is contained in a nilpotent subgroup H, with , is nilpotent provided that either is odd or, if is even, then r is not a Fermât prime.
Finite groups with -quasinormal subgroups.
Finite groups with eight non-linear irreducible characters
This Note contains the complete list of finite groups, having exactly eight non-linear irreducible characters. In section 4 we consider in full details some typical cases.
Finite groups with exactly thirteen conjugacy classes
Finite groups with few conjugacy classes of subgroups
Finite groups with few self-normalizing subgroups
We describe finite groups which contain just one conjugate class of self-normalizing subgroups.
Finite groups with globally permutable lattice of subgroups
The notions of permutable and globally permutable lattices were first introduced and studied by J. Krempa and B. Terlikowska-Osłowska [4]. These are lattices preserving many interesting properties of modular lattices. In this paper all finite groups with globally permutable lattices of subgroups are described. It is shown that such finite p-groups are exactly the p-groups with modular lattices of subgroups, and that the non-nilpotent groups form an essentially larger class though they have a description...
Finite groups with Hall supplements to primitive subgroups.
Finite groups with modular chains
In 1954, Kontorovich and Plotkin introduced the concept of a modular chain in a lattice to obtain a lattice-theoretic characterization of the class of torsion-free nilpotent groups. We determine the structure of finite groups with modular chains. It turns out that this class of groups lies strictly between the class of finite groups with lower semimodular subgroup lattice and the projective closure of the class of finite nilpotent groups.
Finite groups with prime graphs of diameter
In this paper we consider a prime graph of finite groups. In particular, we expect finite groups with prime graphs of maximal diameter.
Finite groups with primitive Sylow normalizers
We prove that are primitive the finite groups whose normalizers of the Sylow subgroups are primitive. We classify the groups of such class, denoted by , and we study the Schunck classes whose boundary is contained in . We give also necessary and sufficient conditions in order that the projectors be subnormally embedded.
Finite Groups with Small Conjugacy Classes.
Finite Groups with some -Permutably Embedded and Weakly -Permutable Subgroups
Let be a finite group, the smallest prime dividing the order of and a Sylow -subgroup of with the smallest generator number . There is a set of maximal subgroups of such that . In the present paper, we investigate the structure of a finite group under the assumption that every member of is either -permutably embedded or weakly -permutable in to give criteria for a group to be -supersolvable or -nilpotent.
Finite groups with some SS-supplemented subgroups
A subgroup of a finite group is said to be SS-supplemented in if there exists a subgroup of such that and is S-quasinormal in . We analyze how certain properties of SS-supplemented subgroups influence the structure of finite groups. Our results improve and generalize several recent results.