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.


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


Zbl 0476.20002