Halfsubgroups
by
Arun S. Muktibodh
Nagpur University, Nagpur, India

In this paper we have investigated some Halfsubgroups of a group which generate a group. Halfsubgroup is a half groupoid S (a partially closed subset) of G in which associativity holds whenever the corresponding products are in S, identity element is in S and each element of S has an inverse in S. Different types of Halfsubgroups generating the group (hsgg) have been defined and certain groups have been studied in terms of their hsggs. Order class of a group with unity forms a typical Halfsubgroup which plays an important role in the further developement of some important results. Finally it is proved that an abelian group whose order is product of distinct primes is a direct product of order classes with unity.

Date received: February 25, 2002

Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caig-83.