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The stabilizer of the group determinant and bounds for Lehmer's conjecture on finite abelian groups

Given a finite group G of cardinality N, the group determinant [theta]G associated to G is a homogeneous polynomial in N variables of degree N. We study two properties of [theta]G. First we determine the stabilizer of [theta](G) under the action of permuting its variables. Then we also prove that the Lehmer's constant for any finite abelian group must satisfy a system of congruence equations. In particular when G is a p-group, we can strengthen the result to establish upper and lower bounds for the Lehmer's constant. / text

Identiferoai:union.ndltd.org:UTEXAS/oai:repositories.lib.utexas.edu:2152/21685
Date23 October 2013
CreatorsVipismakul, Wasin
Source SetsUniversity of Texas
Languageen_US
Detected LanguageEnglish
Formatapplication/pdf

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