Abstract For a mixing shift of finite type, the associated automorphism group has rich algebraic structure, and yet we have few criteria to distinguish when two such groups are isomorphic. We introduce stabilization group, study its properties, use them many stabilized groups. also show that for full shift, subgroup generated by elements order is simple an extension free abelian rank this group.

The Independence Theorem for the congruence lattice and the auto-morphism group of a nite lattice was proved by V. A. Baranski and A. Urquhart. Both proofs utilize the characterization theorem of congruence lattices of nite lattices (as nite distributive lattices) and the characterization theorem of auto-morphism groups of nite lattices (as nite groups). In this paper, we introduce a new, stron...

We determine the quantum automorphism groups of finite graphs. These are quantum subgroups of the quantum permutation groups defined by Wang. The quantum automorphism group is a stronger invariant for finite graphs than the usual automorphism group. We get a quantum dihedral group D4.

Any finite group can be encoded as the automorphism group of an unlabeled simple graph. Recently Hartke, Kolb, Nishikawa, and Stolee (2010) demonstrated a construction that allows any ordered pair of finite groups to be represented as the automorphism group of a graph and a vertexdeleted subgraph. In this note, we describe a generalized scenario as a game between a player and an adversary: an a...

the full automorphism group of $u_6(2)$ is a group of the form $u_6(2){:}s_3$. the group $u_6(2){:}s_3$ has a maximal subgroup $2^9{:}(l_3(4){:}s_3)$ of order 61931520. in the present paper, we determine the fischer-clifford matrices (which are not known yet) and hence compute the character table of the split extension $2^9{:}(l_3(4){:}s_3)$.