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On extending Scott modules

Research output: Thesis › Doctoral Thesis

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On extending Scott modules. / Gullon, Alec.
Lancaster University, 2017. 160 p.

Research output: Thesis › Doctoral Thesis

Harvard

Gullon, A 2017, 'On extending Scott modules', PhD, Lancaster University. https://doi.org/10.17635/lancaster/thesis/155

APA

Gullon, A. (2017). On extending Scott modules. [Doctoral Thesis, Lancaster University]. Lancaster University. https://doi.org/10.17635/lancaster/thesis/155

Vancouver

Gullon A. On extending Scott modules. Lancaster University, 2017. 160 p. doi: 10.17635/lancaster/thesis/155

Author

Gullon, Alec. / On extending Scott modules. Lancaster University, 2017. 160 p.

Bibtex

@phdthesis{ae393073ae8144babff42bde46eefa75,
title = "On extending Scott modules",
abstract = "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.",
author = "Alec Gullon",
year = "2017",
doi = "10.17635/lancaster/thesis/155",
language = "English",
publisher = "Lancaster University",
school = "Lancaster University",

}

RIS

TY - BOOK

T1 - On extending Scott modules

AU - Gullon, Alec

PY - 2017

Y1 - 2017

N2 - 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.

AB - 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.

U2 - 10.17635/lancaster/thesis/155

DO - 10.17635/lancaster/thesis/155

M3 - Doctoral Thesis

PB - Lancaster University

ER -