Year: 2025
Type: preprint
Abstract: Inspired by a conjecture by Guarnieri and Vendramin concerning the number of braces with a generalized quaternion adjoint group, many researchers have studied braces whose adjoint group is a non-abelian $2$-group with a cyclic subgroup of index $2$. Following this direction, braces with generalized quaternion, dihedral, and semidihedral adjoint groups have been classified. It was found that the number of such braces stabilizes as the group order increases. In this paper, we consider the remaining open case of modular maximal-cyclic groups. We show that these braces possess only one non-cyclic additive group structure, and, in contrast to previous findings, the number of such braces increases with increasing order.
Source: arXiv (Cornell University)
Authors: Das, Arpan, Kanrar, Arpan
Language: English
Topic: Advanced Topics in Algebra
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4414458383
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