Counting fuzzy subgroups in particular cases of semi-dihedral group
Author(s):
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:
One of the significant aspects of fuzzy group theory is the classification of the fuzzy subgroups of finite groups. The main goal of this paper is to give an explicit formula for the number of fuzzy subgroups of the semi-dihedral group of order 8n in particular cases n=p^m and n=pq; by using the natural equivalence relation. The corresponding equivalence classes of fuzzy subgroups of the semi-dihedral group are closely connected to the chains of subgroups of the semi-dihedral group. In this regard; Inclusion-Exclusion principle and structure of the maximal subgroups play an essential role and in some situations give relations which lead to explicit formulas. Finally; by the obtained results; we determine the fuzzy subgroups of all semi-dihedral groups of order less than 100.
Keywords:
Language:
Persian
Published:
Journal of Fuzzy Systems and Applications, Volume:6 Issue: 2, 2023
Pages:
215 to 235
https://www.magiran.com/p2755877
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