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On p-saturable groups
- Source :
-
Journal of Algebra . Sep2007, Vol. 315 Issue 2, p809-823. 15p. - Publication Year :
- 2007
-
Abstract
- Abstract: A pro-p group G is a PF-group if it has central series of closed subgroups with trivial intersection satisfying and . In this paper, we prove that a finitely generated pro-p group G is a p-saturable group, in the sense of Lazard, if and only if it is a torsion free PF-group. Using this characterization, we study certain families of subgroups of p-saturable groups. For example, we prove that any normal subgroup of a p-saturable group contained in the Frattini is again p-saturable. [Copyright &y& Elsevier]
- Subjects :
- *GROUP theory
*MATHEMATICS
*ALGEBRA
*ARITHMETIC groups
Subjects
Details
- Language :
- English
- ISSN :
- 00218693
- Volume :
- 315
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 26246381
- Full Text :
- https://doi.org/10.1016/j.jalgebra.2007.02.005