Free products of topological groups with central amalgamation. II
Authors:
M. S. Khan and Sidney A. Morris
Journal:
Trans. Amer. Math. Soc. 273 (1982), 417-432
MSC:
Primary 22A05; Secondary 20E06, 54D50
DOI:
https://doi.org/10.1090/S0002-9947-1982-0667154-7
MathSciNet review:
667154
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Abstract | References | Similar Articles | Additional Information
Abstract: In Free products of topological groups with central amalgamation. I, we introduced the notion of amalgamated free product of topological groups and showed that if is a common central closed subgroup of Hausdorff topological groups
and
, then the amalgamated free product
exists and is Hausdorff. In this paper, we give an alternative much shorter (but less informative) proof of this result. We then proceed to describe the properties of
. In particular, we find necessary and sufficient conditions for
to be a locally compact Hausdorff group, a complete metric group, and a maximally almost periodic group. Properties such as being a Baire space and connectedness are also investigated. In the case that
,
and
are
-groups, the topology of
is fully described. A consequence of this description is that for
-groups
is homeomorphic to
, where
is the direct product of
and
with
amalgamated, and
is the free topological group on the smash product of
and
.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1982-0667154-7
Article copyright:
© Copyright 1982
American Mathematical Society