10 citations · 27 across the 15 of their papers we have counts for
15 papers
Groups satisfying Gaschütz's complement theorem
Stefanos Aivazidis, Benjamin Sambale
A classical theorem of Gaschütz states that an abelian normal subgroup N of a finite group G has a complement in G whenever it has a complement in some subgroup H with $N \leq H \l…
Subgroup bounds for abelian -groups with applications
Stefanos Aivazidis
We prove an upper bound for the number of subgroups of an abelian -group, with constants that are sharp on homocyclic blocks. If has type , the main exponent is $η(λ)=\…
Counting in nilpotent injectors and Carter subgroups
Stefanos Aivazidis, Maria Loukaki, John Shareshian
We investigate number-theoretic properties of the collection of nilpotent injectors or nilpotent projectors containing certain subgroups of finite soluble (or -constr…
Common transversals and complements in abelian groups
Stefanos Aivazidis, Maria Loukaki, Benjamin Sambale
Given a finite abelian group and cyclic subgroups , , of of the same order, we find necessary and sufficient conditions for , , to admit a common transv…
The -series of a -group and complements of abelian subgroups
Stefanos Aivazidis, Maria Loukaki
Let be a -group. We denote by the intersection of all subgroups of having index , for . In this paper, the newly introduced s…
On the common transversal probability in finite groups
S. Aivazidis, M. Loukaki, T. W. Mueller
Let be a finite group, and let be a subgroup of . We compute the probability, denoted by , that a left transversal of in is also a right transversal, thu…
Subgroup congruences for groups of prime power order
Stefanos Aivazidis, Maria Loukaki
Given a -group and a subgroup-closed class , we associate with each -subgroup certain quantities which count -subgroups contain…
A generalisation of Schenkman's theorem
Stefanos Aivazidis, Ina N. Safonova, Alexander N. Skiba
Let be a finite group and let be a hereditary saturated formation. We denote by the product of all normal subgroups of suc…
Finite non-cyclic -groups whose number of subgroups is minimal
Stefanos Aivazidis, Thomas Müller
Recent results of Qu and Tuarnauceanu describe explicitly the finite p-groups which are not elementary abelian and have the property that the number of their subgroups is maximal a…
A note on abelian subgroups of maximal order
Stefanos Aivazidis, Robert M. Guralnick
In a recent paper of the first author and I. M. Isaacs it was shown that if m = m(G) is the maximal order of an abelian subgroup of the finite group G, then |G| divides m! ([AI18,…
Large subgroups in finite groups
Stefanos Aivazidis, Thomas W. Müller
Following Isaacs (see [Isa08, p. 94]), we call a normal subgroup N of a finite group G large, if , so that N has bounded index in G. Our principal aim here is to est…
On residuals of finite groups
Stefanos Aivazidis, Thomas Mueller
A theorem of Dolfi, Herzog, Kaplan, and Lev \cite[Thm.~C]{DHKL} asserts that in a finite group with trivial Fitting subgroup, the size of the soluble residual of the group is bound…
On the Frattini subgroup of a finite group
Stefanos Aivazidis, Adolfo Ballester-Bolinches
We study the class of finite groups satisfying for all normal subgroups of . As a consequence of our main results we extend and amplify a theorem of Do…
On the distribution of the density of maximal order elements in general linear groups
Stefanos Aivazidis, Efthymios Sofos
In this paper we consider the density of maximal order elements in . Fixing any of the rank of the group, the characteristic or the degree of the exte…
On the subgroup permutability degree of the simple Suzuki groups
Stefanos Aivazidis
We prove that the subgroup permutability degree of the simple Suzuki groups vanishes asymptotically. In the course of the proof we establish that the limit of the probability of a…