Finite groups in which -quasinormality is a transitive relation
Finite groups of automorphisms of K3 surfaces and the Mathieu group.
Finite groups of bounded rank with an almost regular automorphism of prime order.
Finite Groups of Exponent 12 as Automorphism Groups.
Finite Groups of Rank 3. I.
Finite Groups of Rank 3. II.
Finite groups whose all proper subgroups are -groups
A group is said to be a -group if for every divisor of the order of , there exists a subgroup of of order such that is normal or abnormal in . We give a complete classification of those groups which are not -groups but all of whose proper subgroups are -groups.
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...