منابع مشابه
Constructive Membership Testing in Black-Box Classical Groups
1 School of Mathematics and Statistics, The University of Western Australia 35 Stirling Highway CRAWLEY WA 6009 Australia [email protected], [email protected] 2 Faculty of Information Sciences and Engineering, The University of Canberra, ACT, 2601 [email protected] 3 Centro de Álgebra da Universidade de Lisboa Av. Prof. Gama Pinto, 2, 1649-003 Lisboa, Portugal csaba.schnei...
متن کاملConstructive membership in black-box groups
We present an algorithm to reduce the constructive membership problem for a black-box group G to three instances of the same problem for involution centralisers in G. If G is a simple group of Lie type in odd characteristic, then this reduction can be performed in (Monte Carlo) polynomial time.
متن کاملRecognising simplicity of black-box groups
We investigate the complexity of computing involutions and their centralizers in groups of Lie type over finite fields of odd order, and discuss applications to the problem of deciding whether a matrix group, or a black-box group of known characteristic, is simple. We show that if the characteristic is odd, then simplicity can be recognised in Monte Carlo polynomial time. Mathematics Subject Cl...
متن کاملCentralisers of Involutions in Black Box Groups
We discuss basic structural properties of finite black box groups. A special emphasis is made on the use of centralisers of involutions in probabilistic recognition of black box groups. In particular, we suggest an algorithm for finding the p-core of a black box group of odd characteristic. This special role of involutions suggest that the theory of black box groups reproduces, at a non-determi...
متن کاملBlack box groups isomorphic to PGL(2,2e)
Article history: Received 13 September 2013 Available online 8 September 2014 Communicated by Charles Leedham-Green MSC: primary 20D06 secondary 20B40, 68Q25
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ژورنال
عنوان ژورنال: Memoirs of the American Mathematical Society
سال: 2001
ISSN: 0065-9266,1947-6221
DOI: 10.1090/memo/0708