Growth of generating sets for direct powers of classical algebraic structures

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)
3 Downloads (Pure)

Abstract

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.
Original languageEnglish
Pages (from-to)105-126
Number of pages22
JournalJournal of the Australian Mathematical Society
Volume89
Issue number1
DOIs
Publication statusPublished - Aug 2010

Keywords

  • Generating sets
  • Growth
  • Direct products
  • Algebraic structures
  • Universal algebra

Fingerprint

Dive into the research topics of 'Growth of generating sets for direct powers of classical algebraic structures'. Together they form a unique fingerprint.

Cite this