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Sylow subgroups of index 2 in their normalizers

Abstract:

The following theorem is proved:

Theorem Let G be a finite group, P a Sylow p-subgroup of G, p odd. Suppose

  1. |N(P)/P⋅C(P)| = 2;
  2. cl(P) ≤ 2 .

Then

  1. if G is perfect, then P is necessarily cyclic;
  2. if P is not cyclic, then either 0p(G) < G, or 02(G) < G with G = 0p,(G)⋅N(P).

A unified proof is given as far as possible, but the proof e...

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Peer review status:
Peer reviewed

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Department:
University of Oxford
Role:
Author
Type of award:
DPhil
Level of award:
Doctoral
Awarding institution:
University of Oxford
Source identifiers:
601870535
UUID:
uuid:391b761e-9802-4fef-819b-512c3daa496e
Local pid:
polonsky:9:1
Deposit date:
2017-10-05

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