Existentially closed locally cofinite groups
1992 ◽
Vol 35
(2)
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pp. 233-253
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Keyword(s):
Let be a class of finite groups. Then a c-group shall be a topological group which has a fundamental system of open neighbourhoods of the identity consisting of normal subgroups with -factor groups and trivial intersection. In this note we study groups which are existentially closed (e.c.) with respect to the class Lc of all direct limits of c-groups (where satisfies certain closure properties). We show that the so-called locally closed normal subgroups of an e.c. Lc-group are totally ordered via inclusion. Moreover it turns out that every ∀2-sentence, which is true for countable e.c. L-groups, also holds for e.c. Lc-groups. This allows it to transfer many known properties from e.c. L-groups to e.c. Lc-groups.
2014 ◽
Vol 14
(01)
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pp. 1550007
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Keyword(s):
1996 ◽
Vol 54
(3)
◽
pp. 369-372
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Keyword(s):
Keyword(s):
2010 ◽
Vol 5
(2)
◽
pp. 211-219
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1980 ◽
Vol 1980
(316)
◽
pp. 83-98
1960 ◽
Vol 12
◽
pp. 73-100
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Keyword(s):
1988 ◽
Vol 150
(1)
◽
pp. 299-309
1999 ◽
Vol 59
(2)
◽
pp. 541-556
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