Splitting Groups with Basis Property

Abstract EN

A finite group G is called splitting or splittable if it is a union of some collections of its proper subgroups intersecting pairwise at the identity.

A special kind of splitting is known to be normal splitting.

Also, a group G is said to have the basis property if, for each subgroup H≤G, H has a basis (minimal generating set), and any two bases have the same cardinality.

In this work, I discuss a relation between classes of finite groups that possess both normal splitting and the basis property.

This paper shows mainly that any non-p-group with basis property is normal splitting.

However, the converse is not true in general.

A counterexample is given.

It is well known that any p-group has basis property.

I demonstrate some types of p-groups which are splitting as well.