The maximal totally bounded group topology on G and the biggest minimal G-space, for Abelian groups G

Polish Groups Topological Groups a Topological Group Is a Group G with a Topology on G for Which the Operations

These notes introduce the reader to Polish groups|topological groups in which the underlying space is Polish. No background in topological groups is assumed, but I will present the material fairly rapidly and leave quite a lot for the reader to check on his or her own. My main motivation for writing such notes arises from the applications and connections in model theory, where closed subgroups ...

Discrete sets and the maximal totally bounded group topology*

Hart, K.P. and J. van Mill, Discrete sets and the maximal totally bounded group topology, Journal of Pure and Applied Algebra 70 (1991) 73-80. If G is an Abelian group, then G # is G with its maximal totally bounded group topology. We prove that every A c G# contains a closed (in G#) and discrete subset B such that lB1 = IAl. This answers a question posed by Eric van Douwen. We also present an ...

The Nonabelian Simple Groups G , \ G \ < 106 — Minimal Generating Pairs

Minimal (k, m, n) generating pairs and their associated presentations are defined for all nonabelian simple groups G, IGI < 10 , excepting the family PSL(2, q). A complete set of minimal (2, m, n) generating permutations of minimal degree is tabulated for these G. The set is complete in the sense that any minimal generating pair for G will satisfy the same presentation as exactly one of the lis...

G-equivalence in group algebras and minimal abelian codes

Let G be a finite abelian group and F a field such that char(F) 6 | |G|. Denote by FG the group algebra of G over F. A (semisimple) abelian code is an ideal of FG. Two codes I1 and I2 of FG are G-equivalent if there exists an automorphism ψ of G whose linear extension to FG maps I1 onto I2. In this paper we give a necessary and sufficient condition for minimal abelian codes to be G-equivalent a...

On the Equivariant Homotopy of Free Abelian Groups on G-spaces and G-spectra