Minimal generating sets of groups, rings, and fields

Halbelsen, L., Hamilton, M. and Ruzicka, P. (2007) Minimal generating sets of groups, rings, and fields. Quaestiones Mathematicae, 30(3), pp. 355-363.

Abstract

A subset X of a group (or a ring, or a field) is called generating, if the smallest subgroup (or subring, or subfield) containing X is the group (ring, field) itself. A generating set X is called minimal generating, if X does not properly contain any generating set. The existence and cardinalities of minimal generating sets of various groups, rings, and fields are investigated. In particular it is shown that there are groups, rings, and fields which do not have a minimal generating set. Among other result, the cardinality of minimal generating sets of finite abelian groups and of finite products of Z(n) rings is computed.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Hamilton, Dr Martin
• Authors: Halbelsen, L., Hamilton, M., and Ruzicka, P.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Quaestiones Mathematicae
• ISSN: 1607-3606