Properties of Auto- and Antiautomorphisms of Maximal Chain Structures and their Relations to i-Perspectivities

Karzel, Helmut; Kosiorek, Jarosław; Matraś, Andrzej

doi:10.1007/s00025-006-0236-y

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Properties Of Maximal Chain Structures1

∈ Gl(v) and F Is Determined By One Of The Following Formulas1

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2009

2022

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Cited by 6 publications

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“…for instance [9](2.7.5)). We recall that all chains C ∈ C and all generators X ∈ G 1 ∪G 2 have the same cardinality which we call the order of the chain structure and that the cardinality of the point set P is the square of the order.…”

Section: Properties Of Maximal Chain Structuresmentioning

confidence: 99%

Automorphisms of Symmetric and Double Symmetric Chain Structures

Karzel¹,

Kosiorek

Matraś

2009

Results. Math.

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Section: Properties Of Maximal Chain Structuresmentioning

confidence: 99%

Automorphisms of Symmetric and Double Symmetric Chain Structures

Karzel¹,

Kosiorek

Matraś

2009

Results. Math.

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“…Let F ∈ ΓA(Y) be defined by (6). By Lemma 3.10, this formula can be rewritten in the form F (x 1 , x 2 ) = (f (x 1 ), gf(x 2 )) with f ∈ ΓA(V), g ∈ GA(V).…”

Section: ∈ Gl(v) and F Is Determined By One Of The Following Formulasmentioning

confidence: 99%

Chain Geometry Determined by the Affine Group

Prażmowski

Sulima

2012

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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Properties of Auto- and Antiautomorphisms of Maximal Chain Structures and their Relations to i-Perspectivities

Abstract: Let E be a non empty set, let P :

Cited by 6 publications

References 5 publications

Automorphisms of Symmetric and Double Symmetric Chain Structures

Automorphisms of Symmetric and Double Symmetric Chain Structures

Chain Geometry Determined by the Affine Group

Helmut Karzel (1928–2021)

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