Local classes and pairwise mutually permutable products of finite groups.
Maximal subclasses of local Fitting classes.
More metanilpotent Fitting classes with bounded chief factor ranks
Multiplicative Dedekind -function and representations of finite groups
In this article we study the problem of finding such finite groups that the modular forms associated with all elements of these groups by means of a certain faithful representation belong to a special class of modular forms (so-called multiplicative products). This problem is open.We find metacyclic groups with such property and describe the Sylow -subgroups, for such groups. We also give a review of the results about the connection between multiplicative -products and elements of finite orders...
Neuer Beweis eines Fundamentaltheorems aus der Theorie der Substitutionslehre
Nonabelian Sylow subgroups of finite groups of even order.
Normal subgroups and projectivities of finite groups
Normality Conditions for Quasinormal Subgroups in Finite Groups.
Note on the -nilpotency in finite groups.
Notes on the average number of Sylow subgroups of finite groups
We show that if the average number of (nonnormal) Sylow subgroups of a finite group is less than then is solvable or . This generalizes an earlier result by the third author.
Odd Automorphisms of Sylow 2-subgroups of sporadic simple groups.
Odd Order Hall Subgroups of GL(n, q) and Sp(2n, q).
Odd order Hall subgroups of the classical linear groups.
On a class of groups with Lagrangian factor groups.
On a generalization of a theorem of Burnside
A theorem of Burnside asserts that a finite group is -nilpotent if for some prime a Sylow -subgroup of lies in the center of its normalizer. In this paper, let be a finite group and the smallest prime divisor of , the order of . Let . As a generalization of Burnside’s theorem, it is shown that if every non-cyclic -subgroup of is self-normalizing or normal in then is solvable. In particular, if , where for and for , then is -nilpotent or -closed.
On a theorem of Frobenius.
On Alperin's fusion theorem.
On complemented subgroups of finite groups
A subgroup of a group is said to be complemented in if there exists a subgroup of such that and . In this paper we determine the structure of finite groups with some complemented primary subgroups, and obtain some new results about -nilpotent groups.
On complete nilpotent groups.
On cover-avoiding subgroups of Sylow subgroups of finite groups