Title: 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 |N(P)/P⋅C(P)| = 2; cl(P) ≤ 2 . Then if G is perfect, then P is necessarily cyclic; if P is not cyclic, then either 0 p (G) 2 (G) p ,(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: |P′| = p, P is abelian but not cyclic, or |P′| > p. Different methods are in fact required for each case. Several corollaries are also discussed.
Publication Year: 1973
Publication Date: 1973-01-01
Language: en
Type: dissertation
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