
TL;DR
This paper investigates the structure of logically cyclic groups, which are groups where a single element can define all others through first-order formulas, exploring their properties and classifications.
Contribution
It provides a detailed analysis of the structure of logically cyclic groups, offering new insights into their definability and classification within group theory.
Findings
Characterization of logically cyclic groups
Identification of conditions for definability
Structural classifications and properties
Abstract
A group is called logically cyclic, if it contains an element such that every element of can be defined by a first order formula with parameter . The aim of this paper is to investigate the structure of such groups.
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