The Upper Central Series of the Unit Group of an Integral Group Ring

Autor:	M. M. Parmenter, Yuanlin Li
Rok vydání:	2005
Předmět:	Combinatorics Unit group Algebra Algebra and Number Theory Torsion (algebra) FC-group Abelian group Mathematics Group ring
Zdroj:	Communications in Algebra. 33:1409-1415
ISSN:	1532-4125 0092-7872
DOI:	10.1081/agb-200061026
Popis:	Let Z n (𝒰) denote the n'th term of the upper central series of the unit group 𝒰 of ℤG and [Ztilde](𝒰) = Z n (𝒰). It is shown that if the set of torsion elements of G forms a subgroup T and [Ztilde](𝒰)⊈C 𝒰(T), then T is either an Abelian 2-group or a Q-group. Moreover, [Ztilde](𝒰) ⊆ G ⋅ C 𝒰(T) whenever G is an FC group. #Communicated by M. Ferrero.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::09d31b6c3569b925b86549b5dbb82f3e https://doi.org/10.1081/agb-200061026 Zobrazit plný text záznamu