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Aufsatz / Paper in SCI-Expanded-Zeitschrift

Polynomial functions and endomorphism near-rings on certain linear groups

Aichinger E., Mayr P.: Polynomial functions and endomorphism near-rings on certain linear groups, in: Communications in Algebra, Volume 31 (11), Page(s) 5627-5651, 2003.

BibTeX

@ARTICLE{
title = {Polynomial functions and endomorphism near-rings on certain linear groups},
type = {Aufsatz / Paper in SCI-Expanded-Zeitschrift},
author = {Aichinger, Erhard and Mayr, Peter},
language = {EN},
abstract = {We describe the unary polynomial functions on the non-solvable groups $G$ with $\SL(n,q) \le G \le \GL(n,q)$ and on their quotients $G/Y$ with $Y \le Z(G)$, and we compute the size of the inner automorphism near-ring $I(G/Y)$. We compare this near-ring to the endomorphism near-ring $E(G/Y)$, and we obtain a full characterization of those $G$ and $Y$ for which $I(G/Y) = E(G/Y)$ holds. For the case $Y = \{1\}$, this characterization yields that we have $E(G) = I(G)$ if and only if $G = \SL(n,q)$. We investigate the automorphism near-ring $A(G)$, and we show that for all non-solvable groups $G$ with $\SL(n,q) \le G \le \GL(n,q)$, we have $I(G) = A(G)$. Our results are based on a description of the polynomial functions on those non-abelian finite groups $G$ that satisfy the following conditions: $G' = G''$, $G/Z(G)$ is centerless, and there is no normal subgroup $N$ of $G$ with $G' \cap Z(G) < N < G'$.},
pages = {5627-5651},
journal = {Communications in Algebra},
volume = {31 (11)},
issn = {0092-7872},
year = {2003},
url = {http://www.dekker.com/servlet/product/productid/AGB},
}

Details

Zusammenfassung: We describe the unary polynomial functions on the non-solvable groups $G$ with $\SL(n,q) \le G \le \GL(n,q)$ and on their quotients $G/Y$ with $Y \le Z(G)$, and we compute the size of the inner automorphism near-ring $I(G/Y)$. We compare this near-ring to the endomorphism near-ring $E(G/Y)$, and we obtain a full characterization of those $G$ and $Y$ for which $I(G/Y) = E(G/Y)$ holds. For the case $Y = \{1\}$, this characterization yields that we have $E(G) = I(G)$ if and only if $G = \SL(n,q)$. We investigate the automorphism near-ring $A(G)$, and we show that for all non-solvable groups $G$ with $\SL(n,q) \le G \le \GL(n,q)$, we have $I(G) = A(G)$. Our results are based on a description of the polynomial functions on those non-abelian finite groups $G$ that satisfy the following conditions: $G' = G''$, $G/Z(G)$ is centerless, and there is no normal subgroup $N$ of $G$ with $G' \cap Z(G) < N < G'$.

Journal: Communications in Algebra
Volume: 31 (11)
Erscheinungsjahr: 2003
Seitenreferenz: 5627-5651
Anzahl Seiten: 25
Web: http://www.dekker.com/servlet/product/productid/AGB (Communications in Algebra)
ISSN: 0092-7872

Beteiligte

AutorInnen / HerausgeberInnen: Assoz.Univprof. DI Dr. Erhard Aichinger, Priv.-Doz. DI Dr. Peter Mayr

Forschungseinheiten der JKU:

Wissenschaftszweige: 101 Mathematik | 101001 Algebra | 101005 Computeralgebra | 101013 Mathematische Logik | 102031 Theoretische Informatik

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