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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 J^{p} = 0, then the ordinary exponential series can be used to show that normalizers of algebra subgroups are strong. If J^{p} 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.
Advisor: | Gagola, Stephen M., Jr. |
Commitee: | |
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 |
Source Type: | DISSERTATION |
Subjects: | Mathematics |
Keywords: | Algebra group, Artin-hasse exponential series, Strong subgroup |
Publication Number: | 10631117 |
ISBN: | 9780355014129 |