For a finite group , the intersection graph of which is denoted by is an undirected graph such that its vertices are all nontrivial proper subgroups of and two distinct vertices and are adjacent when . In this paper we classify all finite groups whose intersection graphs are regular. Also, we find some results on the intersection graphs of simple groups and finally we study the structure of .
Gli autori studiano il sottogruppo intersezione dei sottogruppi massimali e non supersolubili di un gruppo finito e le relazioni tra la struttura di e quella di .
Let G be a finite p-group and let F be the field of p elements. It is shown that if G is elementary abelian-by-cyclic then the isomorphism type of G is determined by FG.
In this paper, we study the situation as to when the unit group U(KG) of a group algebra KG equals K*G(1 + J(KG)), where K is a field of characteristic p > 0 and G is a finite group.
All commutative semigroups are described such that the Jacobson radical is homogeneous in each ring graded by .