Symmetric Groups under multiset perspective

Abstract

A multiset is a collection of objects in which repetition of elements is significant. In this paper an attempt to define a symmetric group under multiset context is presented and the analogous to Cayley's theorem is derived.

Multiset Topological Space as Generalization of the Classical Topological Space via Support Set

“…The research carried out so far shows a strong analogy in the behaviour of classical sets and msets. It is possible to extend some of the main notion and results of sets to the setting of msets ( [11] [12], [13], [14], [15], etc). Girish and John [2], introduced the concept of topological spaces in the context of msets (called an M-topological space).…”

Commutativity and Cancellability of Finite Semi-Multigroups

“…In 2009, Girish and Sunil [3], introduced the concepts of relations, function, composition, and equivalence in msets context. Tella and Daniel ([12], [13]) have considered sets of mappings between msets and studied about symmetric groups under mset perspective. Nazmul et al [6] improved on Tella and Daniel's work and added two axioms which marks the foundations of studying group theory in mset perspective.…”

Characteristic submultigroups of a multigroup

“…The idea is consistent with other non-standard groups in [1] [4], [9], [11], [13], [15], [16], etc. Although other works in [3], [5], [8], [12], [14], [19], [20] earlier used the term multigroup as an extension of group theory (with divergent views), the notion of multigroup in [10] is quite accepted because it agrees with other non-classical groups and defined over multiset (see [7], [17], [18], [21] for details of multisets). Further studies on the concept of multigroups via multisets can be found in [2], [6].…”