Year: 2024
Type: article
Abstract: Let A be an F-central simple algebra of degree $m^2=\prod _{i=1}^k p_i^{2\alpha _i}$ and G be a subgroup of the unit group of A such that $F[G]=A$ . We prove that if G is a central product of two of its subgroups M and N, then $F[M]\otimes _F F[N]\cong F[G]$ . Also, if G is locally nilpotent, then G is a central product of subgroups $H_i$ , where $[F[H_i]:F]=p_i^{2\alpha _i}$ , $A=F[G]\cong F[H_1]\otimes _F \cdots \otimes _F F[H_k]$ and $H_i/Z(G)$ is the Sylow $p_i$ -subgroup of $G/Z(G)$ for each i with $1\leq i\leq k$ . Additionally, there is an element of order $p_i$ in F for each i with $1\leq i\leq k$ .
Authors: R. FALLAH-MOGHADDAM, H. R. DORBIDI
Institutions: Farhangian University, University of Jiroft
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,450
OpenAlex ID: W4404118753