Inner mappings of Bruck loops

被引：18

作者：

Kreuzer, A ^{[1
]}

机构：

[1] Tech Univ Munich, Math Inst, D-80290 Munich, Germany

来源：

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY | 1998年 / 123卷

关键词：

D O I：

10.1017/S0305004197001771

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

K-loops have their origin in the theory of sharply 2-transitive groups. In this paper a proof is given that K-loops and Bruck loops are the same. For the proof it is necessary to show that in a (left) Bruck loop the left inner mappings L(b) L(n) L(ab)(-1) are automorphisms. This paper generalizes results of Glauberman [3], Kist[8] and Kreuzer[9].

引用

页码：53 / 57

页数：5

共 18 条

[1]

[Anonymous], DEMONSTRATIO MATH

[2]

[Anonymous], RESULTS MATH

[3]

Bruck R.H., 1958, SURVEY BINARY SYSTEM

[4] LOOPS WHOSE INNER MAPPINGS ARE AUTOMORPHISMS [J].

BRUCK, RH ;

PAIGE, LJ .

ANNALS OF MATHEMATICS, 1956, 63 (02) :308-323

[5]

FUNK M., 1993, J GEOMETRY, V48, P63

[6]

GLAUBERMAN G, 1966, J ALGEBRA, V1, P374

[7]

KARZEL H, 1968, ABH MATH SEM HAMBURG, V32, P191

[8]

Karzel H., 1993, RESULTS MATH, V23, P338, DOI [10.1007/BF03322306, DOI 10.1007/BF03322306]

[9]

KERBY W, 1971, ABH MATH SEM HAMBURG, V37, P20

[10]

Kikkawa M., 1975, HIROSHIMA MATH J, V5, P141

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