Eine Charakterisierung der zwischenPS-L (2,K) undPGL (2,K) liegenden Permutationsgruppen

Mäurer, Helmut

doi:10.1007/bf01192803

Cited by 4 publications

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“…In [10] Mäurer gives another characterization. Here the notion of Zassenhaus transitivity is needed: A group acts Zassenhaus-transitively on some set if it acts doubly transitively and any triple of pairwise different points has a trivial stabilizer.…”

Section: (I) Fulfills the Conditions (1)-(3): (1) For Any Three Diffementioning

confidence: 97%

“…Using the group action, we first introduce an addition and then a multiplication on the set of points distant to a fixed one. Our line of proof is inspired by Mäurer's in [9,10].…”

Section: Construction Of the Ringmentioning

confidence: 99%

“…Here the notion of Zassenhaus transitivity is needed: A group acts Zassenhaus-transitively on some set if it acts doubly transitively and any triple of pairwise different points has a trivial stabilizer. [10] (ii) ∼ = K , where K is a commutative field with char K = 2, and is a group with…”

Section: (I) Fulfills the Conditions (1)-(3): (1) For Any Three Diffementioning

confidence: 99%

“…Key Words: projective lines over rings; projective groups over rings; permutation groups.In [9] and [10] Mäurer modifies the famous theorem due to Tits that characterizes the permutation groups PGL 2 K over commutative fields among all sharply triply transitive permutation groups. Mäurer's results are based upon the concept of symmetry instead of transitivity.…”

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confidence: 95%

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Projective Groups over Rings

Blunck

2002

Journal of Algebra

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In this paper, Mäurer's theorems characterizing certain subgroups of the projective group PGL 2 K over a field K are generalized to the case of rings. Key Words: projective lines over rings; projective groups over rings; permutation groups.In [9] and [10] Mäurer modifies the famous theorem due to Tits that characterizes the permutation groups PGL 2 K over commutative fields among all sharply triply transitive permutation groups. Mäurer's results are based upon the concept of symmetry instead of transitivity. The aim of the present paper is to carry over Mäurer's theorems to the case of a large class of rings, including the commutative algebras R over a field K such that n = dim K R < ∞ and K > 5n.For the reader's convenience, in Section 1 we recall the theorems by Tits and Mäurer, respectively. Moreover, we introduce the projective line over a ring and groups acting on it. We state a generalization of Tits's theorem for projective groups over rings due to Herzer.In Section 2 we find appropriate generalizations of the conditions used by Mäurer for his characterization of certain subgroups of PGL 2 K . The coordinatization results we are aiming at will require them as axioms. We are concerned with a permutation group acting on a point set and leaving invariant a certain relation on called "distant."1 The results of this paper are part of the author's Habilitationsschrift [3]. I thank the referee for his/her valuable suggestions on how to shorten Section 6. 266

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Section: (I) Fulfills the Conditions (1)-(3): (1) For Any Three Diffementioning

confidence: 97%

“…Using the group action, we first introduce an addition and then a multiplication on the set of points distant to a fixed one. Our line of proof is inspired by Mäurer's in [9,10].…”

Section: Construction Of the Ringmentioning

confidence: 99%

Section: (I) Fulfills the Conditions (1)-(3): (1) For Any Three Diffementioning

confidence: 99%

mentioning

confidence: 95%

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Projective Groups over Rings

Blunck

2002

Journal of Algebra

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“…The other axioms are inspired by those used in [11] and [10] by H. Mäurer (who considered permutation groups, i.e., the case where is the relation =). They imply that the group contains many reflections.…”

Section: Introductionmentioning

confidence: 99%