Costantino Delizia, Mohammad Reza R Moghaddam, Akbar Rhemtulla
May 12, 2006
For any integer n > 1, the variety of n -Bell groups is defined by the law w ( x 1 , x 2 ) = [ x 1 n , x 2 ][ x 1 , x 2 n ] −1 . Bell groups were studied by R. Brandl in , and by R. Brandl and L.-C. Kappe in . In this paper we determine the structure of these groups. We prove that if G is an n -Bell group then G / Z 2 ( G ) has finite exponent depending only on n . Moreover, either G / Z 2 ( G ) is locally finite or G has a finitely generated subgroup H such that H / Z ( H ) is an infinite group of finite exponent. Finally, if G is finitely generated, then the subgroup H may be chosen to be the finite residual of G .