In this paper we survey, also in historical perspective, the results connected with the notion of the commutativity degree of a finite group, i.e., the probability that two randomly selected elements of the group commute.
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In 1985, V. G. Pestov described a neighborhood base at the identity of free topological groups on a Tychonoff space in terms of the elements of the fine uniformity on the Tychonoff space. In this paper, we extend Postev’s description to the free paratopological groups where we introduce a neighborhood base at the identity of free paratopological groups on any topological space in terms of the elements of the fine quasiuniformity on the space.
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