Date of Award
Finite groups, Group theory, relations
Doctor of Philosophy (PhD)
Louis F. McAuley
Science and Mathematics
Subgroups and quotient groups are elementary concepts and at the same time important tools for investigating the structure of groups. Though a group is usually not determined by its proper subgroups and proper quotient groups, significant estimates can often be deduced from information about these derived structures. The information gathered from subgroups on the one hand and quotient groups on the other hand is essentially complimentary in nature. This suggests that subgroups and quotient groups, in a rather general sense, might be considered as dual concepts. This dissertation is concerned with a special form of duality, and we will first review some of the duality concepts in group theory related to the current investigation.
In this dissertation, our emphasis is with Fuchs, Kertész and Szele on duality in terms of the isomorphism types of subgroups and quotient groups. More precisely, in this paper finite groups satisfying condition (A) or (B), or both, are studied. With a slight modification of definitions in , we call groups satisfying condition (A) S- dual groups and groups satisfying condition (B) Q - dual groups. It is also understood, that in this paper, as in , a self-dual group denotes a group satisfying both conditions (A) and (B).
Ying, John Hsiao-I, "Relations between subgroups and quotient groups of finite groups" (1973). Graduate Dissertations and Theses. 216.