# Automorphism Group

### Some articles on group, automorphism group, automorphisms, automorphism:

Binary Tetrahedral Group - Properties
... The binary tetrahedral group, denoted by 2T, fits into the short exact sequence This sequence does not split, meaning that 2T is not a semidirect product of {±1} by T ... The binary tetrahedral group is the covering group of the tetrahedral group ... Thinking of the tetrahedral group as the alternating group on four letters, we thus have the binary tetrahedral group as the covering group, The center of 2T is the subgroup {±1} ...
Automorphisms Of The Symmetric And Alternating Groups - Small n - Alternating
... For n = 1 and 2, A1 = A2 = 1 is trivial, so the automorphism group is also trivial ... For n = 3, A3 = C3 = Z/3 is abelian (and cyclic) the automorphism group is GL(1, Z/3*) = C2, and the inner automorphism group is trivial (because it is abelian) ...
Stable Curve
... a complete connected curve whose only singularities are ordinary double points and whose automorphism group is finite ... The condition that the automorphism group is finite can be replaced by the condition that it is not of arithmetic genus one and every non-singular rational component meets the ... curve is one satisfying similar conditions, except that the automorphism group is allowed to be reductive rather than finite (or equivalently its connected ...
Dynkin Diagram - Automorphisms
... also have self-isomorphisms or "automorphisms" ... Diagram automorphisms correspond to outer automorphisms of the Lie algebra, meaning that the outer automorphism group Out = Aut/Inn equals the group of diagram ... The diagrams that have non-trivial automorphisms are An, Dn, and E6 ...
Automorphisms Of The Symmetric And Alternating Groups - The Exceptional Outer Automorphism of S6 - Other Constructions
... Ernst Witt found a copy of Aut(S6) in the Mathieu group M12 (a subgroup T isomorphic to S6 and an element σ that normalizes T and acts by outer automorphism) ... Similarly to S6 acting on a set of 6 elements in 2 different ways (having an outer automorphism), M12 acts on a set of 12 elements in 2 different ways (has an ... The full automorphism group of A6 appears naturally as a maximal subgroup of the Mathieu group M12 in 2 ways, as either a subgroup fixing a division of the 12 points into a pair of 6-element sets, or as a subgroup ...

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