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Title: On extending Scott modules
Author: Gullon, Alec
ISNI:       0000 0004 6423 5538
Awarding Body: Lancaster University
Current Institution: Lancaster University
Date of Award: 2017
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We study a variety of questions related to the Scott modules S(G,Q) associated to a finite group G, where Q denotes a p-subgroup of G for a given prime p. The main concept we study is that of a p-extendible group, which we define to be a group in which the dimension of S(G,Q) is minimal for all p-subgroups Q of G. We study those Frobenius groups which are p-extendible and complete a classification of the local subgroups of the sporadic groups which are p-extendible. Furthermore, we study Scott modules associated to finite classical groups which admit (B,N)-pairs that are split at characteristic p. The thesis concludes with some considerations about the second relative syzygy with respect to a subgroup Q for a certain class of p-groups P.
Supervisor: Mazza, Nadia Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral