Growth of generating sets for direct powers of classical algebraic structures
MetadataShow full item record
For an algebraic structure A denote by d(A) the smallest size of a generating set for A, and let d(A)=(d(A),d(A2),d(A3),…), where An denotes a direct power of A. In this paper we investigate the asymptotic behaviour of the sequence d(A) when A is one of the classical structures—a group, ring, module, algebra or Lie algebra. We show that if A is finite then d(A) grows either linearly or logarithmically. In the infinite case constant growth becomes another possibility; in particular, if A is an infinite simple structure belonging to one of the above classes then d(A) is eventually constant. Where appropriate we frame our exposition within the general theory of congruence permutable varieties.
Quick , M & Ruskuc , N 2010 , ' Growth of generating sets for direct powers of classical algebraic structures ' Journal of the Australian Mathematical Society , vol 89 , no. 1 , pp. 105-126 . , 10.1017/S1446788710001473
Journal of the Australian Mathematical Society
(c) 2010 Australian Mathematical Publishing Association Inc.
Items in the St Andrews Research Repository are protected by copyright, with all rights reserved, unless otherwise indicated.