STUDY OF MULTIGROUP AND ITS EXTENSIONS
STUDY OF MULTIGROUP AND ITS EXTENSIONS
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Date
2016-08
Authors
GIWA, JAMILATU SHEHU
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Abstract
Multigroup is a generalization of classical group. The concept of multigroup* was introduced by reversing the conditions of multigroup. We established a tabular representation of multigroup space and multigroup* space and defined the terms semimultigroup and semimultigroup* spaces that culminated into the partition of the spaces. The construction of multigroup and multigroup* spaces shows that the existence and the multiplicity of the identity element plays a vital role in identifying a multigroup within a multiset space. The formula ๐ ๐๐๐ข๐ ๐๐๐๐ก๐๐๐๐๐ (๐ยก) for calculating the total number of submultigroups and submultigroups* found in a complex multigroup and complex multigroup* spaces was derived. Finally, the operations in multigroup were extended to multigroup* and it was found that the intersection of two multigroups* is not a multigroup* whereas the union of two multigroups* is a multigroup* against the perspective in multigroup.
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A THESIS SUBMITTED TO THE SCHOOL OF POSTGRADUATE STUDIES, AHMADU BELLO UNIVERSITY, ZARIA, NIGERIA
IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE AWARD OF A MASTER DEGREE IN MATHEMATICS
DEPARMENT OF MATHEMATICS,
AHMADU BELLO UNIVERSITY, ZARIA
NIGERIA
Keywords
STUDY,, MULTIGROUP,, EXTENSIONS,