Joseph Kirtland

Direct products of inseparable finite groups, II

Necessary and sufficient conditions are established for when a finite group can be written as the direct product of nontrivial inseparable groups and for when all other decompositions give rise to such a direct product decomposition.

Finite solvable multiprimitive groups

The investigation of the structure of finite solvable multiprimitive groups through an induced geometry leads to a classification of finite solvable multiprimitive groups of up to derived length 3 and to a necessary and sufficient geometric condition for when a finite solvable nC-group is multiprimitive. An application is made to finite groups which have all their splitting systems equivalent.

The geometry of finite groups through the use of splitting systems

The spliting systems of a finite group are used to induce a geometry associated with the group. The method generalizes the classical approach used to induce a geometry associated with a finite dimensional vector space and extends concepts related to the special and projective linear groups to arbitrary finite groups. Applications are made to finite solvable nC-groups and to the automorphism group of homocyclic abelian p-groups.

Finite separable metacyclic 2-groups

Abstract A finite separable metacyclic 2-group G can be written as the semidirect product of a cyclic group with another cyclic group. Necessary and sufficient conditions are given for when all other split decompositions of G result in, up to isomorphism, this same semidirect product representation for G .