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M. P. Gállego, P. Hauck, and M. D. Pérez-Ramos
2-Engel relations between subgroups
J. Algebra, 447:31–55, 2016
https://doi.org/10.1016/j.jalgebra.2015.08.030
Abstract
In this paper we study groups G generated by two subgroups A and B such that 〈a, b〉 is nilpotent of class at most 2 for all a∈A and b∈B . A detailed description of the structure of such groups is obtained, generalizing the classical result of Hopkins and Levi on 2-Engel groups.
2010 Mathematical Subject Classification: Primary 20F45; Secondary 20F18, 20D15, 20F12
Keywords: 2-Engel condition, 2-generated subgroups, L-connection, Nilpotency class