Some topological properties of residually Černikov groups
1982 ◽
Vol 23
(1)
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pp. 65-82
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Keyword(s):
In this paper we shall indicate how to generalise the concept of a cofinite group (see [7]). We recall that any residually finite group can be made into a topological group by taking as a basis of neighbourhoods of the identity precisely the normal subgroups of finite index. The class of compact cofinite groups is then easily seen to be the class of profinite groups, where a group is profinite if and only if it is an inverse limit of finite groups. It turns out that every cofinite group can be embedded as a dense subgroup of a profinite group. This has important consequences for the class of countable locally finite-soluble groups with finite Sylow p-subgroups for all primes p, as shown in [7] and [14].
2011 ◽
Vol 03
(02)
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pp. 153-160
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2005 ◽
Vol 15
(03)
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pp. 571-576
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Keyword(s):
2002 ◽
Vol 45
(3)
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pp. 717-721
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2011 ◽
Vol 84
(1)
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pp. 159-170
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Keyword(s):
1995 ◽
Vol 38
(3)
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pp. 511-522
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Keyword(s):
1977 ◽
Vol 24
(3)
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pp. 339-349
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Keyword(s):
1996 ◽
Vol 60
(2)
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pp. 222-227
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Keyword(s):
1989 ◽
Vol 106
(3)
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pp. 385-388
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