Let G = SkwrSn be the wreath product of two symmetric groups Sk and Sn. We prove that every normalized automorphism θ of the integral group ring G can be written in the form θ = γ°τu, where γ is an automorphism of G and τu denotes the inner automorphism induced by a unit ...
For n > 3, except for n = 6, the automorphism group of An is the symmetric group Sn, with inner automorphism group An and outer automorphism group Z2; the outer automorphism comes from conjugation by an odd permutation. 对n > 3,除了 n = 6,An 的自同构群就是 Sn 的自同构...
We prove that the automorphism groups of Mg,n and are isomorphic to the symmetric group on n elements Sn for any g, n such that 2g - 2 + n ≥ 3, and compute the remaining cases.doi:10.1112/jlms/jdt057Massarenti AlexOxford University PressJournal of the London Mathematical Society...
(sic) Z(2) similar or equal to (A(n) (sic) S-n) (sic) Z(2), where R(A(n)) is the right regular representation of An, Inn(Sn) is the inner automorphism group of Sn, and Z2 = (h), where h is the map alpha (bar right arrow) alpha(-1) (VCZ is an element of An)...
First, we define a new hyperoperation on Sn and study its properties. Next, we prove that (Sn, is a single-power cyclic hypergroup with finite period. Then, we determine the set of all automorphisms of (Sn, ) and prove that it is a finite group under the operation of function ...
Automorphisms of graphsCayley graphsTransposition setsModified bubble-sort graphLet S be a set of transpositions that generates the symmetric group Sn, where n≥3. The transposition graph T(S) is defined to be the graph with vertex set {1,…,n} and with vertices i and j being adjacent in...
For any integersn≥3, the automorphism groups of bipartite Kneser type-1 graphs are isomorphic to the symmetric groupSn. The bipartite Kneser type-1 graph's Wiener index, peripheral Wiener index, and peripheral Hosoya polynomial were established. For integersnandk,n>2and2k...
We prove that all these graphs are holomorphic, thus that their automorphism group is AutGamma = L( Sn )AutS Sn , except for the one such that the transposition graph of S, denoted TS, is a square or a complete graph of order greater than 2. We will show also that AutS Sn ≃...
The fixed group of an automorphism of a word hyperbolic group is rational - Neumann - 1992 () Citation Context ...ly embedded codimension two sphere Sn ∞ ↩→ Sn+2 ∞ . We need to show it is unknotted. First note that Proposition 2.1 in [14] shows that the fixed set of τ∞ ...
Here Sn denotes the symmetric group on n elements.doi:10.1112/plms/s3-69.2.225Matatyahu RubinProceedings of the London Mathematical SocietyM. RUBIN, 'On the reconstruction of K0-categorical structure from their automorphism group', preprint, University of Beer Sheva, 1987....