Exploratory Results on Finite Topological Groups

On p-topological groups

“…Since the basis of topology on finite left (right) topological group is cosets of a subgroup (partition topology) [1] and for the partition topology τ on any set X, τ p is P(X ) and so every subset of X is pre-open. -Every topological group is p-topological group, but converse need not be true.…”

“…Based on this, some generalizations of topological groups such as paratopological groups, semitopological groups and quasitopological groups are defined. In a finite group, all the above mentioned generalizations coincide [1]. The concepts of S-topological group and s-topological group were discussed in [10] and the theory of almost topological group was initiated in [11].…”