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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| Format: | Article |
| Language: | English |
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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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| _version_ | 1850159877525078016 |
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| author | Peter Hilton Robert Militello |
| author_facet | Peter Hilton Robert Militello |
| author_sort | Peter Hilton |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-b970c7ecd9c14e80b2008d7d0df56979 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1996-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-b970c7ecd9c14e80b2008d7d0df569792025-08-20T02:23:19ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251996-01-0119353954410.1155/S0161171296000749On almost finitely generated nilpotent groupsPeter Hilton0Robert Militello1Department of Mathematical Sciences, State University of New York, Binghamton 13902-6000, NY, USADepartment of Mathematics, Rhodes College, Memphis 38112-1690, TN, USAA 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.http://dx.doi.org/10.1155/S0161171296000749 |
| spellingShingle | Peter Hilton Robert Militello On almost finitely generated nilpotent groups International Journal of Mathematics and Mathematical Sciences |
| title | On almost finitely generated nilpotent groups |
| title_full | On almost finitely generated nilpotent groups |
| title_fullStr | On almost finitely generated nilpotent groups |
| title_full_unstemmed | On almost finitely generated nilpotent groups |
| title_short | On almost finitely generated nilpotent groups |
| title_sort | on almost finitely generated nilpotent groups |
| url | http://dx.doi.org/10.1155/S0161171296000749 |
| work_keys_str_mv | AT peterhilton onalmostfinitelygeneratednilpotentgroups AT robertmilitello onalmostfinitelygeneratednilpotentgroups |