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＜電子ブック＞
Group and Ring Theoretic Properties of Polycyclic Groups / by B.A.F. Wehrfritz
(Algebra and Applications. ISSN:21922950 ; 10)

版	1st ed. 2009.
出版者	(London : Springer London : Imprint: Springer)
出版年	2009
本文言語	英語
大きさ	VIII, 128 p : online resource
著者標目	*Wehrfritz, B.A.F author SpringerLink (Online service)
件　名	LCSH:Group theory LCSH:Associative rings LCSH:Associative algebras LCSH:Commutative algebra LCSH:Commutative rings FREE:Group Theory and Generalizations FREE:Associative Rings and Algebras FREE:Commutative Rings and Algebras
一般注記	Some Basic Group Theory -- The Basic Theory of Polycyclic Groups -- Some Ring Theory -- Soluble Linear Groups -- Further Group-Theoretic Properties of Polycyclic Groups -- Hypercentral Groups and Rings -- Groups Acting on Finitely Generated Commutative Rings -- Prime Ideals in Polycyclic Group Rings -- The Structure of Modules over Polycyclic Groups -- Semilinear and Skew Linear Groups Polycyclic groups are built from cyclic groups in a specific way. They arise in many contexts within group theory itself but also more generally in algebra, for example in the theory of Noetherian rings. They also touch on some aspects of topology, geometry and number theory. The first half of this book develops the standard group theoretic techniques for studying polycyclic groups and the basic properties of these groups. The second half then focuses specifically on the ring theoretic properties of polycyclic groups and their applications, often to purely group theoretic situations. The book is not intended to be encyclopedic. Instead, it is a study manual for graduate students and researchers coming into contact with polycyclic groups, where the main lines of the subject can be learned from scratch by any reader who has been exposed to some undergraduate algebra, especially groups, rings and vector spaces. Thus the book has been kept short and readable with a view that it can be read and worked through from cover to cover. At the end of each topic covered there is a description without proofs, but with full references, of further developments in the area. The book then concludes with an extensive bibliography of items relating to polycyclic groups HTTP:URL=https://doi.org/10.1007/978-1-84882-941-1

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