On the galois number and the minimal degree of doubly transitive groups

Epkenhans, Martin; Gerstengarbe, Oliver

doi:10.1080/00927870008827129

Cited by 3 publications

(3 citation statements)

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“…We briefly give the list below. A good description of them can be found in [6,7]. Moreover, also their 2-transitive permutation representations are known, and this is a fact that we need in our approach.…”

Section: Classif Ication Of Operator Groupsmentioning

confidence: 99%

“…For most of the cases above this goes quite smoothly. Below we give a table which yields for each of the 2-transitive groups/representations G the number φ(G), equal to the maximal number of points fixed by an element which does not act as the identity, and the number of elements N (G) contained in the module on which G acts, see [7].…”

Section: Classif Ication Of Operator Groupsmentioning

confidence: 99%

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The 2-Transitive Transplantable Isospectral Drums

Schillewaert

Thas

2011

SIGMA

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Abstract. For Riemannian manifolds there are several examples which are isospectral but not isometric, see e.g. J. Milnor [Proc. Nat. Acad. Sci. USA 51 (1964), 542]; in the present paper, we investigate pairs of domains in R 2 which are isospectral but not congruent. All known such counter examples to M. Kac's famous question can be constructed by a certain tiling method ("transplantability") using special linear operator groups which act 2-transitively on certain associated modules. In this paper we prove that if any operator group acts 2-transitively on the associated module, no new counter examples can occur. In fact, the main result is a corollary of a result on Schreier coset graphs of 2-transitive groups.

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Section: Classif Ication Of Operator Groupsmentioning

confidence: 99%

Section: Classif Ication Of Operator Groupsmentioning

confidence: 99%

The 2-Transitive Transplantable Isospectral Drums

Schillewaert

Thas

2011

SIGMA

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“…Also if G is a subgroup of the symmetric group S n and G contains a 3-cycle but no transposition then g = n − 2 . For more on calculating Galois numbers see [1,5,8].…”

Section: Their Proof Like That Of the Earlier Conner Theorem On Tracmentioning

confidence: 99%