PROFINITE TOPOLOGIES IN FREE PRODUCTS OF GROUPS
2004 ◽
Vol 14
(05n06)
◽
pp. 751-772
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Let [Formula: see text] be a nonempty class of finite groups closed under taking subgroups, quotients and extensions. We consider groups G endowed with their pro-[Formula: see text] topology, and say that G is 2-subgroup separable if whenever H and K are finitely generated closed subgroups of G, then the subset HK is closed. We prove that if the groups G1 and G2 are 2-subgroup separable, then so is their free product G1*G2. This extends a result to T. Coulbois. The proof uses actions of groups on abstract and profinite trees.
2001 ◽
Vol 11
(03)
◽
pp. 281-290
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Keyword(s):
1999 ◽
Vol 09
(05)
◽
pp. 521-528
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Keyword(s):
Keyword(s):
1979 ◽
Vol 31
(6)
◽
pp. 1329-1338
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1970 ◽
Vol 3
(1)
◽
pp. 85-96
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1966 ◽
Vol 62
(2)
◽
pp. 129-134
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Keyword(s):
2006 ◽
Vol 81
(2)
◽
pp. 199-208
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Keyword(s):
1995 ◽
Vol 38
(1)
◽
pp. 120-127
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