منابع مشابه
Maximal harmonic group actions on finite graphs
This paper studies groups of maximal size acting harmonically on a finite graph. Our main result states that these maximal graph groups are exactly the finite quotients of the modular group Γ = 〈 x, y | x = y = 1 〉 of size at least 6. This characterization may be viewed as a discrete analogue of the description of Hurwitz groups as finite quotients of the (2, 3, 7)-triangle group in the context...
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Consider the question: which finite groups operate as symmetries of the complex projective plane P’(C)? Any finite subgroup of &X,(C) acts as a group of collineations and these give the linear models. The list of such groups is relatively short [MBD] but contains, for example, a groups of rank < 2, subgroups of U(Z), and the simple groups A,, A,, an PSL(F,). It turns out that these linear group...
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Let M K be the Kervaire manifold: a closed, piecewise linear (PL) manifold with Kervaire invariant 1 and the same homology as the product S × S of spheres. We show that a finite group of odd order acts freely on M K if and only if it acts freely on S × S. If MK is smoothable, then each smooth structure on MK admits a free smooth involution. If k 6= 2 − 1, then M K does not admit any free TOP in...
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The theory of nonabelian cohomology is used to show that the set of fixed points of a finite group acting on a Siegel modular space is a union of Shimura varieties
متن کاملHalf-Transitive Group Actions on Finite Graphs of Valency 4
The action of a subgroup G of automorphisms of a graph X is said to be 2 -transitive if it is vertexand edgebut not arc-transitive. In this case the graph X is said to be (G, 2)-transitive. In particular, X is 1 2 -transitive if it is (Aut X, 1 2)-transitive. The 2 -transitive action of G on X induces an orientation of the edges of X which is preserved by G. Let X have valency 4. An even length...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1988
ISSN: 0021-8693
DOI: 10.1016/0021-8693(88)90203-7