Abstract
Motivated by the well-known conjecture of Andrews and Curtis Amer. Math. Monthly 73: 2128, 1966., we consider the question of how, in a given n-generator group G, any ordered n-tuple of 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 can be transformed into a generating n-tuple. We obtain upper estimates for the recalcitrance of n-generator finite groupsthus quantifying a result from Borovik, Lubotzky, and Myasnikov, Progr. Math. 248: 1530, 2005and of a wide class of n-generator solvable groups, thus extending and correcting a result from Burns, Herfort, Kam, Macedoska, and Zalesskii, Bull. Austral. Math. Soc. 60: 245251, 1999.
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