Editors: Campbell, Robertson and Smith's Groups St Andrews 2001 in Oxford, Vol 2 PDF

By Editors: Campbell, Robertson and Smith

ISBN-10: 0511065612

ISBN-13: 9780511065613

ISBN-10: 0521537401

ISBN-13: 9780521537407

Show description

Read Online or Download Groups St Andrews 2001 in Oxford, Vol 2 PDF

Best education books

Download PDF by Harold Davis: Building Research Tools with Google For Dummies (For Dummies

It teaches me many beneficial google tips that i did not comprehend ahead of. particularly this www. googlefight. com site is enjoyable. you could struggle something there. Even this e-book with different google similar books.

See who wins.

Download PDF by Alexander M. Samsonov: Strain Solitons in Solids and How to Construct Them

Professor Gerard Maugin in: (ASME) utilized Mechanics reports, Vol. fifty four, No. four, July 2001, pp. B61-B62.

On Mahler and Britten: Essays in Honour of Donald Mitchell by Philip Reed, Donald Mitchell, Britten-Pears Library PDF

In February 1995 Donald Mitchell, the major authority at the existence and works of Gustav Mahler and Benjamin Britten, celebrated his seventieth birthday. This paintings is released to mark this occasion. extraordinary composers, students, colleagues and buddies from world wide have written on elements of the 2 composers closest to Mitchell's center - Mahler and Britten - to supply a quantity which not just displays the various most recent considering on them yet which additionally will pay tribute to the influence of Mitchell's personal paintings on those composers over the past 50 years.

Additional info for Groups St Andrews 2001 in Oxford, Vol 2

Example text

R(G, V ) (where r(G, V ) is as in Section 2), are representatives of the orbits 322 KELLER of G on V , then r(G,V ) (1) k(CG (vi )) = k(GV ) = i=1 1 |G| |CG (v)| k(CG (v)). v∈V Alternatively, if gi , i = 1, . . , k(G) are representatives of the conjugacy classes of G, then k(G) (2) r(CG (gi ), CV (gi )) = k(GV ) = i=1 1 |G| |CG (g)| r(CG (g), CV (g)). g∈G These elegant formulas look meaningful and seem to be a key to the solution of the k(GV )–problem, but surprisingly in the development up to this point they have hardly been used at all, except for settling easy cases such as G abelian (see [109]) or more recently in [36] to solve the case p = 31.

The point of this is that the existence of weakly real vectors is strong enough to yield the wanted conclusion k(GV ) ≤ |V |, but it is still weak enough to be true for all GV at least if p is sufficiently large. And its key property is that unlike the property k(GV ) ≤ |V | it has a good inductive behaviour which makes the inductive proof possible. So it is just about the “right” property to look at. Other properties like the existence of regular orbits, which also imply k(GV ) ≤ |V |, are too strong and even for large p simply are not always satisfied, and correspondingly their inductive behaviour is not good enough.

All these results indicate that dl(G) might grow slower than linearly with |cd(G)|. As it happens, the results on orbit sizes presented above shed some more light on the question. Namely if V is a G–module, then so is V0 = Irr(V ), and we consider the semidirect product GV0 . 18)] every λ ∈ V0 can be extended to its inertia group in GV , from which it can be induced to an irreducible character of GV . This shows that every orbit size of G on V0 is a complex irreducible character degree of GV . Using this allows a translation of results on orbit sizes to results on character degrees.

Download PDF sample

Groups St Andrews 2001 in Oxford, Vol 2 by Editors: Campbell, Robertson and Smith


by David
4.1

Rated 4.32 of 5 – based on 35 votes