For any integer n > 1, the variety of n-Bell groups is defined by the law [x^n,y][x,y^n]^{-1}. Bell groups were studied by R. Brandl, and by R. Brandl and L.-C. Kappe. 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.
The structure of Bell groups
DELIZIA, Costantino;
2006-01-01
Abstract
For any integer n > 1, the variety of n-Bell groups is defined by the law [x^n,y][x,y^n]^{-1}. Bell groups were studied by R. Brandl, and by R. Brandl and L.-C. Kappe. 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.File in questo prodotto:
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