Vol. 58, No. 2, 1975

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Transitive affine transformations on groups

David W. Jonah and Bertram Manuel Schreiber

Vol. 58 (1975), No. 2, 483–509

An affine transformation T on a group G is an automorphism followed by a translation; T is transitive if for each x,y G there is an integer n such that Tn(x) = y. All groups with transitive affine transformations are determined: the infinite cyclic and infinite dihedral group are the only infinite examples; while the finite examples are semi-direct products of certain odd-order groups by a cyclic, dihedral or quaternion 2-group. The automorphism groups of the above groups are described, and the automorphisms which occur as parts of transitive affine transformations are given.

Mathematical Subject Classification
Primary: 20F15
Received: 22 May 1974
Published: 1 June 1975
David W. Jonah
Bertram Manuel Schreiber