We shall determine the uniquely existing extension of the alternating group of degree 6 (being normal in the group) by a cyclic group of order 4, which can act on a complex K3 surface.

Some optimal codes related to graphs invariant under the alternating group A8

We show that Y. Prokhorov’s “Simple Finite Subgroups of the Cremona Group of Rank 3” implies that, over any field of characteristic 0, the essential dimensions of the alternating group, A7, and the symmetric group, S7, are 4.

Examples suggest that there is a correspondence between L-spaces and 3manifolds whose fundamental groups cannot be left-ordered. In this paper we establish the equivalence of these conditions for several large classes of such manifolds. In particular, we prove that they are equivalent for any closed, connected, orientable, geometric 3-manifold that is non-hyperbolic, a family which includes all...

In this paper, we establish Schur-Weyl reciprocity for the q-analogue of the alternating group. We analyze the sign q-permutation representation of the Hecke algebra HQ(q),r(q) on the rth tensor product of Z2-graded Q-vector space V = V0⊗V1 in detail, and examine its restriction to the qanalogue of the alternating group H1Q(q),r(q). In consequence, we find out that if dimV0 = dimV1, then the ce...

Recently, Stanley [Longest alternating subsequences of permutations, preprint, arXiv/0511419v1] studied the length of the longest alternating subsequence of a permutation in the symmetric group,where a sequencea, b, c, d, . . . isalternating ifa >bd < · · ·. In this paper, we extend this result to the case of k-ary words. More precisely, we find an explicit formula for the generating functio...

Here we prove that the alternating group of degree n is a faithful completion Goldschmidt G3-amalgam if and only ifn?{1,2,3,4,5,7,8,9,11,12,16,17,19,23}.