caa a22 4500 38809172X CHVBK 20180307125253.0 cr unu---uuuuu 161130e199910 xx s 000 0 eng 10.1017/S0004972700036388 doi S0004972700036388 pii (NATIONALLICENCE)cambridge-10.1017/S0004972700036388 Recalcitrance in groups [Elektronische Daten] 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. Copyright © Australian Mathematical Society 1999 Burns R.G. Department of Mathematics and Statistics, York University, Toronto, Canada M3J 1P3 Herfort W.N. Institut für Angew. Mathematik, Technische Universität, A-1040 Vienna, Austria Kam S.-M Kwi Shing Estate, New Territories, Hong Kong, China Macedońska O. Institute of Mathematics, Silesian Technical University, 44-100 Gliwice, Poland Zalesskii P.A. Department of Mathematics, University of Brasilia, 70910-900 Brasilia-DF, Brazil Bulletin of the Australian Mathematical Society Cambridge University Press 60/2(1999-10), 245-251 0004-9727 60:2<245 1999 60 BAZ https://doi.org/10.1017/S0004972700036388 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0004972700036388 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Burns R.G. Department of Mathematics and Statistics, York University, Toronto, Canada M3J 1P3 NATIONALLICENCE 700 1- Herfort W.N. Institut für Angew. Mathematik, Technische Universität, A-1040 Vienna, Austria NATIONALLICENCE 700 1- Kam S.-M Kwi Shing Estate, New Territories, Hong Kong, China NATIONALLICENCE 700 1- Macedońska O. Institute of Mathematics, Silesian Technical University, 44-100 Gliwice, Poland NATIONALLICENCE 700 1- Zalesskii P.A. Department of Mathematics, University of Brasilia, 70910-900 Brasilia-DF, Brazil NATIONALLICENCE 773 0- Bulletin of the Australian Mathematical Society Cambridge University Press 60/2(1999-10), 245-251 0004-9727 60:2<245 1999 60 BAZ CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge