Point Symmetric 2-Structures

Abstract. In a symmetric 2-structure Σ = (P, G1, G2, K) we fix a chain E ∈ K and define on E two binary operations "+" and "·". Then (E, +) is a K-loop and for E * := E\{o}, (E * , ·) is a Bol loop. If Σ is even point symmetric then (E, +, ·) is a quasidomain and one has the set Af f (E, +,Af f (E, +, ·) one can reproduce via a "chain derivation" the point symmetric 2-structure Σ.Mathematics Subject Classification (1991). 51A99.

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“…In [7] we showed if Σ is of class III then any two orthogonal chains intersect (in exactly one point) and called Σ point symmetric.…”

Section: Chain Structuresmentioning

confidence: 99%

A Representation of a Point Symmetric 2-Structure by a Quasi-Domain

Karzel¹,

Kosiorek

Matraś

2013

Results. Math.

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Helmut Karzel (1928–2021)

et al. 2022

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in Burgwedel, Germany, at the age of 93. He will always be in our best memories as teacher, friend and valued member of the worldwide community of mathematicians. Our deepest sympathy goes out to his three children Dörte, Herbert, Barnim and to Gisela, his partner over the last years.Helmut Karzel was born on January 15, 1928, in Schöneck in Westpreußen, Poland. He spent his youth in Posen, where he attended school from 1934 to 1945. During the last year of World War II he had to serve as flak helper. At the end of the war he was advised to go west. So, in 1945 he reached the German town of Magdeburg, where an uncle lived. There, in 1946, he took the "Abitur" at the Otto von Guericke Schule. His mother and two of his three siblings had to flee from Posen and all of them met again in Magdeburg. 0123456789().: V,-volH. Havlicek et al. J. Geom. By crossing several occupation zone boundaries (at night), Karzel reached Freiburg, Germany, in 1947. He received the admission to study mathematics and physics at the University of Freiburg. Prior to his studies, he was obliged to help for eight weeks in clearing up the rubble of the bomb attacks. Among Karzel's teachers in Freiburg was Emanuel Sperner, who became Professor at the University of Bonn in 1950. Karzel moved to Bonn and obtained his doctorate under Sperner's supervision in 1951. That year he also received the Hausdorff Memorial Prize, which is awarded annually by the University of Bonn for the best dissertation in mathematics of the past academic year.

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Point Symmetric 2-Structures

Cited by 2 publications

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A Representation of a Point Symmetric 2-Structure by a Quasi-Domain

A Representation of a Point Symmetric 2-Structure by a Quasi-Domain

Helmut Karzel (1928–2021)

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