On Hyper (Abelian of Finite Rank) Groups
Keyword(s):
We study the class of groups G, each of whose non-trivial images contains a non-trivial abelian normal subgroup of finite rank. This is very much wider than the class, studied earlier by Robinson and others, of hyperabelian groups H with finite abelian section rank. Our main results are that these groups G are hypercentral by residually finite and are divisible by hypo(abelian of finite exponent). They need not be divisible by residually finite, unlike the groups H above. In practice, we work with a somewhat wider but less easily described class of groups.
Keyword(s):
1969 ◽
Vol 10
(3-4)
◽
pp. 497-498
◽
Keyword(s):
1989 ◽
Vol 106
(3)
◽
pp. 385-388
◽
1969 ◽
Vol 23
(1)
◽
pp. 5-5
1968 ◽
Vol 11
(3)
◽
pp. 371-374
◽
Keyword(s):
Keyword(s):
1999 ◽
Vol 60
(2)
◽
pp. 177-189
◽
Keyword(s):