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math.GR2001
The Andrews-Curtis Conjecture and Black Box Groups
Alexandre V. Borovik, Evgenii I. Khukhro, Alexei G. Myasnikov
The paper discusses the Andrews-Curtis graph of a normal subgroup N in a group G. The vertices of the graph are k-tuples of elements in N which generate N as a normal subgroup; two…
math.GR2001
Centralisers of Involutions in Black Box Groups
Alexandre V. Borovik
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 gr…
math.GR2001
Orthogonal and Symplectic Black Box Groups, Revisited
Alexandre V. Borovik
We propose a simple one sided Monte-Carlo algorithm to distinguish, to any given degree of certainty, between certain symplectic and orthogonal groups over fields of odd order. The…