Nilpotence relations in products of groups

Abstract

Two subgroups 𝐴 and 𝐵 of a group 𝐺 are said to be 𝒩-connected if, for all 𝑎 in 𝐴 and 𝑏 in 𝐵, the subgroup generated by 𝑎 and 𝑏 is a nilpotent group. In this paper, we study the structure of a group 𝐺 assuming that G=AB and 𝐴 and 𝐵 are 𝒩-connected subgroups satisfying Max or Min.

Arithmetic graphs and the products of finite groups

“…Recall that N denotes the class of all nilpotent groups. Following Carocca [6] subgroups H and K are called N-connected if x, y ∈ N for every x ∈ H and y ∈ K. Products of N-connected subgroups were studied in [6,9,10] and other. Here we prove Theorem 1.…”