Generators for finite groups with a unique minimal normal subgroup
Scriviamo ed . Cerchiamo gruppi con generatori tali che ed per alcuni numeri naturali , .
In this paper we classify finite groups with disconnected intersection graphs of subgroups. This solves a problem posed by Csákány and Pollák.
We discuss some examples of nonassociative algebras which occur in VOA (vertex operator algebra) theory and finite group theory. Methods of VOA theory and finite group theory provide a lot of nonassociative algebras to study. Ideas from nonassociative algebra theory could be useful to group theorists and VOA theorists.
In the present paper, we classify groups with the same order and degree pattern as an almost simple group related to the projective special linear simple group . As a consequence of this result we can give a positive answer to a conjecture of W. J. Shi and J. X. Bi, for all almost simple groups related to except . Also, we prove that if is an almost simple group related to except and is a finite group such that and , then .