On Slender Generalized Groups

2025/11/18 by Zand, Mohammad Reza Ahmadi, Ardakani, Hamid Torabi
Computer Science · Decision Sciences · Mathematics · #FOS: Mathematics #Fuzzy and Soft Set Theory #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #semigroups and automata theory

paper · doi:10.48550/arxiv.2511.14498

openalex publication_date 2025/11/18 · openalex created_date 2025/11/20 · openalex updated_date 2026/07/28

Abstract

This paper introduces the concept of slender generalized groups, extending the classical notion of slender abelian groups to the setting of generalized groups (completely simple semigroups). We establish fundamental properties of slender generalized groups and prove that, in the abelian case, the classical and generalized definitions of slenderness coincide. Several structural results are provided, including the behavior of slenderness under homomorphisms and subgroups. We also present examples and non-examples to illustrate the theory. Our results demonstrate that slenderness is preserved under taking generalized subgroups and that the group components G_e(a) of a slender generalized group are slender in the classical sense.

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