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The conjugacy of triality subgroups of Sylow subloops of Moufang loops
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Stephen M. Gagola
Published/Copyright:
May 30, 2010
Abstract
We show that if G is a finite group with triality S and L is the corresponding Moufang loop with P1, P2 ∈ Sylp(L) for a ‘Sylow prime’ p then there exist p-subgroups Q1, Q2 ⩽ G that are conjugate in G such that Qi is invariant under S and Pi is the corresponding Moufang loop for i ∈ {1, 2}. If L is simple, or if 3 does not divide |L|, then the elements of {G(P) ⩽ G| P ∈ Sylp(L)} are conjugate in G and can be permuted transitively by CG(S), hence |Sylp(L)| divides |CG(S)|.
Received: 2009-03-10
Revised: 2010-01-03
Published Online: 2010-05-30
Published in Print: 2010-November
© de Gruyter 2010
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Articles in the same Issue
- The power graph of a finite group, II
- On p-Brauer characters of p′-degree and self-normalizing Sylow p-subgroups
- Finite groups whose irreducible characters vanish on at most three conjugacy classes
- The conjugacy of triality subgroups of Sylow subloops of Moufang loops
- On two questions of L. A. Shemetkov concerning hypercyclically embedded subgroups of finite groups
- Periodic patterns in the graph of p-groups of maximal class
- Lower bounds for representation growth
- Reflexive group topologies on Abelian groups
- On abstract commensurators of groups
- On the SQ-universality of groups with special presentations
