Vol. 9, No. 4, 2016

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Rings of invariants for the three-dimensional modular representations of elementary abelian $p$-groups of rank four

Théo Pierron and R. James Shank

Vol. 9 (2016), No. 4, 551–581

We show that the rings of invariants for the three-dimensional modular representations of an elementary abelian p-group of rank four are complete intersections with embedding dimension at most five. Our results confirm the conjectures of Campbell, Shank and Wehlau (Transform. Groups 18 (2013), 1–22) for these representations.

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modular invariant theory, elementary abelian $p$-groups
Mathematical Subject Classification 2010
Primary: 13A50
Received: 22 October 2014
Revised: 30 June 2015
Accepted: 17 August 2015
Published: 6 July 2016

Communicated by Ravi Vakil
Théo Pierron
Département Mathématiques
ENS Rennes
35170 BRUZ
R. James Shank
School of Mathematics, Statistics & Actuarial Science
University of Kent
United Kingdom