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Recalcitrance in groups

Published online by Cambridge University Press:  17 April 2009

R.G. Burns ,
W.N. Herfort ,
S.-M. Kam ,
O. Macedońska  and
P.A. Zalesskii
R.G. Burns
Affiliation:
Department of Mathematics and Statistics, York University, Toronto, Canada M3J 1P3
W.N. Herfort
Affiliation:
Institut für Angew. Mathematik, Technische Universität, A-1040 Vienna, Austria
S.-M. Kam
Affiliation:
Kwi Shing Estate, New Territories, Hong Kong, China
O. Macedońska
Affiliation:
Institute of Mathematics, Silesian Technical University, 44-100 Gliwice, Poland
P.A. Zalesskii
Affiliation:
Department of Mathematics, University of Brasilia, 70910-900 Brasilia-DF, Brazil
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Motivated by a well-known conjecture of Andrews and Curtis, we consider the question as to how in a given n-generator group G, a given set of n “annihilators” of G, that is, with normal closure all of G, can be transformed by standard moves into a generating n-tuple. The recalcitrance of G is defined to be the least number of elementary standard moves (”elementary M-transformations”) by means of which every annihilating n-tuple of G can be transformed into a generating n-tuple. We show that in the classes of finite and soluble groups, having zero recalcitrance is equivalent to nilpotence, and that a large class of 2-generator soluble groups has recalcitrance at most 3. Some examples and remarks are included.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 60 , Issue 2 , October 1999 , pp. 245 - 251
Copyright
Copyright © Australian Mathematical Society 1999

References

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