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
| Identifer | oai:union.ndltd.org:UTEXAS/oai:repositories.lib.utexas.edu:2152/21685 |
| Date | 23 October 2013 |
| Creators | Vipismakul, Wasin |
| Source Sets | University of Texas |
| Language | en_US |
| Detected Language | English |
| Format | application/pdf |
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