Cyclic intersections and control of fusion

Let H be a subgroup of a finite group G , and suppose that H contains a Sylow p -subgroup P of G . Write N = N G ( H ) , and assume that the Sylow p -subgroups of H ∩ H g are cyclic for all elements g ∈ G not lying in N . We show that in this situation, N controls G -fusion in P .

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Bibliographic Details
Published in:Archiv der Mathematik 2019-12, Vol.113 (6), p.561-563
Main Authors: Isaacs, I. M., Kızmaz, M. Yasir
Format: Article
Language:English
Subjects:
Intersections
Mathematics
Mathematics and Statistics
Subgroups
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Description
Summary:Let H be a subgroup of a finite group G , and suppose that H contains a Sylow p -subgroup P of G . Write N = N G ( H ) , and assume that the Sylow p -subgroups of H ∩ H g are cyclic for all elements g ∈ G not lying in N . We show that in this situation, N controls G -fusion in P .
ISSN:0003-889X
1420-8938
DOI:10.1007/s00013-019-01359-w