5,356 research outputs found
Growth of generating sets for direct powers of classical algebraic structures
No full textFor 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.Peer reviewe
Author's Quick Files
No full textThe Quick Files feature was discontinued and it’s files were migrated into this Project on March 11, 2022. The file URL’s will still resolve properly, and the Quick Files logs are available in the Project’s Recent Activity
author's Quick Files
No full textThe Quick Files feature was discontinued and it’s files were migrated into this Project on March 11, 2022. The file URL’s will still resolve properly, and the Quick Files logs are available in the Project’s Recent Activity
Author's Quick Files
No full textThe Quick Files feature was discontinued and it’s files were migrated into this Project on March 11, 2022. The file URL’s will still resolve properly, and the Quick Files logs are available in the Project’s Recent Activity
author's Quick Files
No full textThe Quick Files feature was discontinued and it’s files were migrated into this Project on March 11, 2022. The file URL’s will still resolve properly, and the Quick Files logs are available in the Project’s Recent Activity
Author's Quick Files
No full textThe Quick Files feature was discontinued and it’s files were migrated into this Project on March 11, 2022. The file URL’s will still resolve properly, and the Quick Files logs are available in the Project’s Recent Activity
author's Quick Files
No full textThe Quick Files feature was discontinued and it’s files were migrated into this Project on March 11, 2022. The file URL’s will still resolve properly, and the Quick Files logs are available in the Project’s Recent Activity
Submission author's Quick Files
No full textThe Quick Files feature was discontinued and it’s files were migrated into this Project on March 11, 2022. The file URL’s will still resolve properly, and the Quick Files logs are available in the Project’s Recent Activity
JAP author's Quick Files
No full textThe Quick Files feature was discontinued and it’s files were migrated into this Project on March 11, 2022. The file URL’s will still resolve properly, and the Quick Files logs are available in the Project’s Recent Activity
JAP author's Quick Files
No full textThe Quick Files feature was discontinued and it’s files were migrated into this Project on March 11, 2022. The file URL’s will still resolve properly, and the Quick Files logs are available in the Project’s Recent Activity
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