We show under MA(ฯ -centered) the existence of at least (2 ฯ ) + non-homeomorphic topological group topologies on the free Abelian group of size 2 ฯ which make it countably compact and separable. In particular, under GCH the maximum possible number of such topologies is attained. As a corollary, we
Topologies on the subgroup lattice of a compact group
โ Scribed by Claus Scheiderer
- Publisher
- Elsevier Science
- Year
- 1986
- Tongue
- English
- Weight
- 645 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0166-8641
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๐ SIMILAR VOLUMES
In this paper, a formula is given for the Mo bius number +(1, S n ) of the subgroup lattice of the symmetric group S n . This formula involves the Mo bius numbers of certain transitive subgroups of S n . When n has at most two (not necessarily distinct) prime factors or n is a power of two, this for
Let M M be the lattice of length 2 with n G 1 atoms. It is an open problem to n ลฝ decide whether or not every such lattice or indeed whether or not every finite . lattice can be represented as an interval in the subgroup lattice of some finite group. We complete the work of the second author, Lucchi