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Fuzzy cyclic subgroups and fuzzy cyclic \(p\)-subgroups. (English) Zbl 0843.20056

The paper presents definitions of fuzzy cyclic subgroups and fuzzy cyclic \(p\)-subgroups. These are new names but not new notions [cf. P. S. Das, J. Math. Anal. Appl. 84, 264-269 (1981; Zbl 0476.20002)]. Namely fuzzy cyclic groups are characterised as fuzzy subgroups of a cyclic group (theorem 3.2). So the new name is superfluous. It should be mentioned that the presented definitions 2.4, 2.10, 3.1 and 4.1 are incomplete.

MSC:

20N25 Fuzzy groups
20E07 Subgroup theorems; subgroup growth
20D15 Finite nilpotent groups, \(p\)-groups

Citations:

Zbl 0476.20002
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