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Characterization of small polygroups by their fundamental groups

    https://doi.org/10.1142/S1793830919500472Cited by:1 (Source: Crossref)

    In this paper, we consider polygroup P,,1,1P,,1,1 and prove necessary and sufficient conditions such that PP is non-commutative. Then by using the Maple programming, we obtain all polygroups of order less than five up to isomorphism. In fact, we determine all 115 non-isomorphic polygroups of order less than five and characterize them by their fundamental groups, i.e., polygroups with same fundamental group, say GG, classifies in the class [G][G]. Finally, we obtain that the fundamental groups of 94 polygroups are the trivial group. The numbers of polygroups in classes [2] and [3] are 16 and 3, respectively, and the classes [2×2] and [4] are singleton.

    AMSC: 20N20