منابع مشابه
Algorithms for computing with nilpotent matrix groups over infinite domains
We develop methods for computing with matrix groups defined over a range of infinite domains, and apply those methods to the design of algorithms for nilpotent groups. In particular, we provide a practical nilpotency testing algorithm for matrix groups over an infinite field. We also provide algorithms to answer a number of structural questions for a nilpotent matrix group.The main algorithms h...
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In this paper we investigate the structure of groups as in the title. Our work builds on work of several other authors, namely Konyuh [5], Leedham-Green and Plesken [6], and Zalesskii [10], who have described the abstract isomorphism types of the groups. We obtain more detailed descriptions, in particular explaining how group structure depends on the existence of an abelian primitive subgroup. ...
متن کاملDecomposing Nilpotent Hessenberg Varieties over Classical Groups
Hessenberg varieties are a family of subvarieties of the flag variety, including the Springer fibers, the Peterson variety, and the entire flag variety itself. The seminal example arises from numerical analysis and consists, for a fixed linear operator M , of the full flags V1 ( V2 . . . ( Vn in GLn with MVi ⊆ Vi+1 for all i. In this paper, I show that all nilpotent Hessenberg varieties in type...
متن کاملVANISHING HOMOLOGY OVER NILPOTENT GROUPS i
Let rr be a nilpotent group and let M be a 77-module. Under certain finiteness assumptions we prove that the twisted homology groups H .(77, M) vanish for all positive i whenever H (n, M) = 0. The purpose of this note is to prove the following vanishing theorem: (1) Theorem. Let rr be a finitely generated nilpotent group, and let Al be a rr-module which is finitely generated over Z[rr]. Assume ...
متن کامل2-step Nilpotent Lie Groups Arising from Semisimple Modules
Let G0 denote a compact semisimple Lie algebra and U a finite dimensional real G0 module. The vector space N0 = U ⊕ G0 admits a canonical 2-step nilpotent Lie algebra structure with [N0,N0] = G0 and an inner product 〈, 〉, unique up to scaling, for which the elements of G0 are skew symmetric derivations of N0. Let N0 denote the corresponding simply connected 2-step nilpotent Lie group with Lie a...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society
سال: 2001
ISSN: 1446-7887,1446-8107
DOI: 10.1017/s1446788700002858