A subgroup X of a group G is closed in the profinite topology if it can be obtained as intersection of a collection of subgroups of finite index of G. It is proved that if all subgroups of infinite rank of a group G are closed, then either G has finite rank or all its subgroups are closed, provided that either G is nilpotent-by-finite or it has finite conjugacy classes.
Groups whose subgroups of infinite rank are closed in the profinite topology / DE FALCO, Maria; DE GIOVANNI, Francesco; Musella, Carmela. - In: REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS, FÍSICAS Y NATURALES. SERIE A, MATEMÁTICAS. - ISSN 1578-7303. - 110:(2016), pp. 565-571. [10.1007/s13398-015-0249-z]
Groups whose subgroups of infinite rank are closed in the profinite topology
DE FALCO, MARIA;DE GIOVANNI, FRANCESCO;MUSELLA, CARMELA
2016
Abstract
A subgroup X of a group G is closed in the profinite topology if it can be obtained as intersection of a collection of subgroups of finite index of G. It is proved that if all subgroups of infinite rank of a group G are closed, then either G has finite rank or all its subgroups are closed, provided that either G is nilpotent-by-finite or it has finite conjugacy classes.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
