On Finite Nilpotent Matrix Groups over Integral Domains
نویسندگان
چکیده
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...
متن کاملNilpotent Primitive Linear Groups over Finite Fields
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 کاملNILPOTENT p-LOCAL FINITE GROUPS
In this paper we provide characterizations of p-nilpotency for fusion systems and p-local finite groups that are inspired by known result for finite groups. In particular, we generalize criteria by Atiyah, Brunetti, Frobenius, Quillen, Stammbach and Tate.
متن کاملRecognizing finite matrix groups over infinite fields
Article history: Received 12 January 2012 Accepted 10 April 2012 Available online 15 June 2012
متن کاملCounting Nilpotent Pairs in Finite Groups
Let G be a nite group and let i (G) denote the proportion of ordered pairs of G that generate a subgroup of nilpotency class i. Various properties of the i 's are established. In particular it is shown that i = k i jGj=jGj 2 for some non-negative integers k i and that P 1 i=1 i is either 1 or at most 1/2 for solvable groups.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: ISRN Algebra
سال: 2013
ISSN: 2090-6293
DOI: 10.1155/2013/638623