Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Zand, Mohammad Reza Ahmadi, Ardakani, Hamid Torabi
Institutions: Yazd University, Ferdowsi University of Mashhad
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7106129554
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