Saturated fusion systems and finite groups
This thesis is primarily concerned with saturated fusion systems over groups of shape q\(^r\) : q where q = p\(^n\) for some odd prime p and some natural number n. We shall present two results related to these fusion systems. Our first result is a complete classification of saturated fusion systems...
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ndltd-bl.uk-oai-ethos.bl.uk-4463482019-04-03T06:32:59ZSaturated fusion systems and finite groupsClelland, Murray Robinson2007This thesis is primarily concerned with saturated fusion systems over groups of shape q\(^r\) : q where q = p\(^n\) for some odd prime p and some natural number n. We shall present two results related to these fusion systems. Our first result is a complete classification of saturated fusion systems over a Sylow p-subgroup of SL\(_3\)(q) (which has shape q\(^3\) : q). This extends a result of Albert Ruiz and Antonio Viruel, who studied the case when q = p in [36]. As an immediate consequence of this result we shall have a complete classification of p-local finite groups over Sylow p-subgroups of SL\(_3\)(q). In the second half of this thesis we shall construct an infinite family of exotic fusion systems over some groups of shape p\(^r\) : p. This extends some work of Broto, Levi and Oliver, who studied the case when r = 3 in [12].512.23QA MathematicsUniversity of Birminghamhttps://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.446348http://etheses.bham.ac.uk//id/eprint/70/Electronic Thesis or Dissertation |
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512.23 QA Mathematics |
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512.23 QA Mathematics Clelland, Murray Robinson Saturated fusion systems and finite groups |
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This thesis is primarily concerned with saturated fusion systems over groups of shape q\(^r\) : q where q = p\(^n\) for some odd prime p and some natural number n. We shall present two results related to these fusion systems. Our first result is a complete classification of saturated fusion systems over a Sylow p-subgroup of SL\(_3\)(q) (which has shape q\(^3\) : q). This extends a result of Albert Ruiz and Antonio Viruel, who studied the case when q = p in [36]. As an immediate consequence of this result we shall have a complete classification of p-local finite groups over Sylow p-subgroups of SL\(_3\)(q). In the second half of this thesis we shall construct an infinite family of exotic fusion systems over some groups of shape p\(^r\) : p. This extends some work of Broto, Levi and Oliver, who studied the case when r = 3 in [12]. |
author |
Clelland, Murray Robinson |
author_facet |
Clelland, Murray Robinson |
author_sort |
Clelland, Murray Robinson |
title |
Saturated fusion systems and finite groups |
title_short |
Saturated fusion systems and finite groups |
title_full |
Saturated fusion systems and finite groups |
title_fullStr |
Saturated fusion systems and finite groups |
title_full_unstemmed |
Saturated fusion systems and finite groups |
title_sort |
saturated fusion systems and finite groups |
publisher |
University of Birmingham |
publishDate |
2007 |
url |
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.446348 |
work_keys_str_mv |
AT clellandmurrayrobinson saturatedfusionsystemsandfinitegroups |
_version_ |
1719013176706596864 |