QUASIRANDOM GROUP ACTIONS
نویسندگان
چکیده
منابع مشابه
Group Actions
The symmetric groups Sn, alternating groups An, and (for n ≥ 3) dihedral groups Dn behave, by their very definition, as permutations on certain sets. The groups Sn and An both permute the set {1, 2, . . . , n} and Dn can be considered as a group of permutations of a regular n-gon, or even just of its n vertices, since rigid motions of the vertices determine where the rest of the n-gon goes. If ...
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There are a number of results of group theory presented in Herstein [1] (the counting principles in Sections 2.5 and 2.11, Cayley’s theorem in Section 2.9 and the Sylow theorems of Section 2.12, among others) whose proofs follow similar ideas. However, it is not apparent that this is so. This handout covers the ideas necessary to tie these results together. The important idea is that of an acti...
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In this paper we study finite group extensions represented by special cohomology classes. As an application, we obtain some restrictions on finite groups which can act freely on a product of spheres or on a product of real projective spaces. In particular, we prove that if (Z/p)r acts freely on (S1)k , then r ≤ k.
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Babai and Sos have asked whether there exists a constant c > 0 such that every finite group G has a product-free subset of size at least c|G|: that is, a subset X that does not contain three elements x, y and z with xy = z. In this paper we show that the answer is no. Moreover, we give a simple sufficient condition for a group not to have any large product-free subset.
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ژورنال
عنوان ژورنال: Forum of Mathematics, Sigma
سال: 2016
ISSN: 2050-5094
DOI: 10.1017/fms.2016.8