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On the Frattini and upper near Frattini subgroups of a generalized free product
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R. B. J. T. Allenby
Published/Copyright:
May 21, 2008
Abstract
It has been conjectured that the Frattini subgroup and the upper (and hence lower) near Frattini subgroup of a generalized free product are contained in the amalgamated subgroup. This paper adds to the results so far obtained by proving, as a corollary to a much more general result, that the conjectured result holds if the amalgamated subgroup is countable.
Received: 2006-07-07
Revised: 2007-07-26
Published Online: 2008-05-21
Published in Print: 2008-May
© de Gruyter 2008
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Articles in the same Issue
- Extending real-valued characters of finite general linear and unitary groups on elements related to regular unipotents
- Involution models of finite Coxeter groups
- Prime divisors of character degrees
- A characterization of HN
- Symmetric groups and conjugacy classes
- Conjugacy classes of non-normal subgroups in finite nilpotent groups
- Normalizers of subgroups of division rings
- On the Frattini and upper near Frattini subgroups of a generalized free product
- Reflection principle characterizing groups in which unconditionally closed sets are algebraic
