Dissertation/Thesis Abstract

Applications of the Artin-Hasse Exponential Series And its Generalizations to Finite Algebra Groups
by Kracht, Darci L., Ph.D., Kent State University, 2011, 67; 10631117
Abstract (Summary)

If F is a finite field of characteristic p and order q and J is a finite-dimensional nilpotent associative F-algebra, then we call the finite p-group G = 1+J an F-algebra group. A subgroup H of G is called an algebra subgroup if H = 1+A for some subalgebra A of J. A subgroup K of G is said to be strong if the order of the intersection of K with H is a power of q for all algebra subgroups H of G. If Jp = 0, then the ordinary exponential series can be used to show that normalizers of algebra subgroups are strong. If Jp is not equal to 0, then the exponential series does not make sense, but a generalization, the Artin-Hasse exponential series, is defined. We use the Artin-Hasse series to determine when normalizers of algebra subgroups are strong and when counter-examples exist. In addition, we give a description of strong subgroups in terms of stringent power series, that is, power series whose linear coefficient and constant term are both 1.

Indexing (document details)
Advisor: Gagola, Stephen M., Jr.
School: Kent State University
Department: College of Arts and Sciences / Department of Mathematical Science
School Location: United States -- Ohio
Source: DAI-B 78/11(E), Dissertation Abstracts International
Subjects: Mathematics
Keywords: Algebra group, Artin-hasse exponential series, Strong subgroup
Publication Number: 10631117
ISBN: 9780355014129
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