Near Frattini subgroups of residually finite generalized free products of groups
2001 ◽
Vol 26
(2)
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pp. 117-121
Keyword(s):
LetG=A★HBbe the generalized free product of the groupsAandBwith the amalgamated subgroupH. Also, letλ(G)andψ(G)represent the lower near Frattini subgroup and the near Frattini subgroup ofG, respectively. IfGis finitely generated and residually finite, then we show thatψ(G)≤H, providedHsatisfies a nontrivial identical relation. Also, we prove that ifGis residually finite, thenλ(G)≤H, provided: (i)Hsatisfies a nontrivial identical relation andA,Bpossess proper subgroupsA1,B1of finite index containingH; (ii) neitherAnorBlies in the variety generated byH; (iii)H<A1≤AandH<B1≤B, whereA1andB1each satisfies a nontrivial identical relation; (iv)His nilpotent.
1972 ◽
Vol 15
(4)
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pp. 569-573
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2015 ◽
Vol 20
(1)
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pp. 133-137
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1993 ◽
Vol 36
(3)
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pp. 296-302
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1971 ◽
Vol 12
(1)
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pp. 21-34
Keyword(s):
1960 ◽
Vol 1
(3)
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pp. 299-310
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2015 ◽
Vol 20
(1)
◽
pp. 124-132
Keyword(s):
1989 ◽
Vol 32
(1)
◽
pp. 11-17
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2011 ◽
Vol Vol. 13 no. 4
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1975 ◽
Vol 47
(2)
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pp. 300-300
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