University of Jiroft | hamidreza dorbidi

Research

Title	LOCALLY NILPOTENT SUBGROUPS OF GLn(D)
Type	Article
Keywords	division ring, locally nilpotent subgroup, central product of groups, crossed product.
Researchers	Reza Fallah-Moghaddam, hamidreza dorbidi

Abstract

Let A be an F-central simple algebra of degree m2 = 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] ⊗F F[N] F[G]. Also, if G is locally nilpotent, then G is a central product of subgroups Hi, where [F[Hi] : F] = p2αi i , A = F[G] F[H1] ⊗F · · · ⊗F F[Hk] and Hi/Z(G) is the Sylow pi-subgroup of G/Z(G) for each i with 1 ≤ i ≤ k. Additionally, there is an element of order pi in F for each i with 1 ≤ i ≤ k.