Finite Groups with All Maximal Subgroups of Prime or Prime Square Index

In this thesis finite groups whose maximal subgroups are of prime or prime square index are studied. The main problem considered is to find out to what extent this property is inherited by subgroups. The principal results are: this property is inherited by all subgroups if the group considered has odd order. This is not necessarily true if the group has even order. Let n be a positive integer. A group G of even order is constructed which contains a subgroup H, and H contains a maximal subgroup W with |H:W| larger than n