#### Vol. 3, No. 4, 2009

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The essential dimension of the normalizer of a maximal torus in the projective linear group

### Aurel Meyer and Zinovy Reichstein

Vol. 3 (2009), No. 4, 467–487
##### Abstract

Let $p$ be a prime, $k$ a field of characteristic $\ne p$ and $N$ the normalizer of the maximal torus in the projective linear group ${PGL}_{n}$. We compute the exact value of the essential dimension ${ed}_{k}\left(N;p\right)$ of $N$ at $p$ for every $n\ge 1$.

##### Keywords
essential dimension, central simple algebra, character lattice, finite p-group, Galois cohomology
##### Mathematical Subject Classification 2000
Primary: 11E72
Secondary: 20D15, 16K20
##### Milestones
Received: 9 September 2008
Revised: 5 December 2008
Accepted: 19 December 2008
Published: 15 June 2009
##### Authors
 Aurel Meyer Department of Mathematics University of British Columbia 1984 Mathematics Road Vancouver, BC  V6T 1Z2 Canada http://www.math.ubc.ca/~aurel Zinovy Reichstein Department of Mathematics University of British Columbia 1984 Mathematics Road Vancouver, BC  V6T 1Z2 Canada http://www.math.ubc.ca/~reichst