4 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)=\…
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,…