Use this URL to cite or link to this record in EThOS: https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.473279
Title: Sylow subgroups of index 2 in their normalizers
Author: Smith, Stephen D.
ISNI:       0000 0001 3462 6405
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 1973
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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 eventually splits into three cases, with hypothesis (2) strengthened by one of:

  1. |P'| = p,
  2. P is abelian but not cyclic, or
  3. |P'| > p.

Different methods are in fact required for each case. Several corollaries are also discussed.

Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.473279  DOI: Not available
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