Characterization of small polygroups by their fundamental groups

Autor:	Dariush Heidari, Bijan Davvaz
Rok vydání:	2019
Předmět:	Maple Pure mathematics Fundamental group 010102 general mathematics engineering Discrete Mathematics and Combinatorics Order (group theory) 010103 numerical & computational mathematics 0101 mathematics engineering.material Characterization (mathematics) 01 natural sciences Mathematics
Zdroj:	Discrete Mathematics, Algorithms and Applications. 11:1950047
ISSN:	1793-8317 1793-8309
DOI:	10.1142/s1793830919500472
Popis:	In this paper, we consider polygroup [Formula: see text] and prove necessary and sufficient conditions such that [Formula: see text] 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 [Formula: see text], classifies in the class [Formula: see text]. Finally, we obtain that the fundamental groups of 94 polygroups are the trivial group. The numbers of polygroups in classes [Formula: see text] and [Formula: see text] are 16 and 3, respectively, and the classes [Formula: see text] and [Formula: see text] are singleton.
Databáze:	OpenAIRE
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