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Title: Perfect isometry groups for blocks of finite groups
Author: Ruengrot, Pornrat
ISNI:       0000 0004 2713 9117
Awarding Body: University of Manchester
Current Institution: University of Manchester
Date of Award: 2011
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Our aim is to investigate perfect isometry groups, which are invariants for blocks of finite groups. There are two subgoals. First is to study some properties of perfect isometry groups in general. We found that every perfect isometry has essentially a unique sign. This allowed us to show that, in many cases, a perfect isometry group contains a direct factor generated by -id. The second subgoal is to calculate perfect isometry groups for various blocks. Notable results include the perfect isometry groups for blocks with defect 1, abelian p-groups, extra special p-groups, and the principal 2-block of the Suzuki group Sz(q). In the case of blocks with defect 1, we also showed that every perfect isometry can be induced by a derived equivalence. With the help of a computer, we also calculated perfect isometry groups for some blocks of sporadic simple groups.Apart from perfect isometries, we also investigated self-isotypies in the special case where C_G(x) is a p-group whenever x is a p-element. We applied our result to calculate isotypies in cyclic p-groups and the principal 2-blocks of the Suzuki group Sz(q).
Supervisor: Eaton, Charles ; Symonds, Peter Sponsor: The Royal Thai Government
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: perfect isometries ; isotypies