On almost finitely generated nilpotent groups
A nilpotent group G is fgp if Gp, is finitely generated (fg) as a p-local group for all primes p; it is fg-like if there exists a nilpotent fg group H such that Gp≃Hp for all primes p. The fgp nilpotent groups form a (generalized) Serre class; the fg-like nilpotent groups do not. However, for abelia...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1996-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171296000749 |
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| Summary: | A nilpotent group G is fgp if Gp, is finitely generated (fg) as a p-local group for all primes
p; it is fg-like if there exists a nilpotent fg group H such that Gp≃Hp for all primes p. The fgp nilpotent
groups form a (generalized) Serre class; the fg-like nilpotent groups do not. However, for abelian
groups, a subgroup of an fg-like group is fg-like, and an extension of an fg-like group by an fg-like group
is fg-like. These properties persist for nilpotent groups with finite commutator subgroup, but fail in
general. |
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| ISSN: | 0161-1712 1687-0425 |