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 ...
متن کاملGroup Actions
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...
متن کاملGroup Actions and Group Extensions
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.
متن کاملTwisted Symmetric Group Actions
Let K be any field, K(x1, . . . , xn) be the rational function field of n variables over K, and Sn and An be the symmetric group and the alternating group of degree n respectively. For any a ∈ K \ {0}, define an action of Sn on K(x1, . . . , xn) by σ · xi = xσ(i) for σ ∈ An and σ · xi = a/xσ(i) for σ ∈ Sn \ An. Theorem. For any field K and n = 3, 4, 5, the fixed field K(x1, . . . , xn) Sn is ra...
متن کاملTransitive Group Actions
Every action of a group on a set decomposes the set into orbits. The group acts on each of the orbits and an orbit does not have sub-orbits (unequal orbits are disjoint), so the decomposition of a set into orbits could be considered as a “factorization” of the set into “irreducible” pieces for the group action. Our focus here is on these irreducible parts, namely group actions with a single orbit.
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2016
ISSN: 0002-9939,1088-6826
DOI: 10.1090/proc/13018