Abstract
If G is a finite group and if A is a group of automorphisms of G whose fixed point subgroup is C G (A) then every subgroup F of C G (A) acts on the set of orbits of A in G. The peculiarities of this action are used here to derive several results on the number of orbits of A in an economical manner.
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Original Russian Text Copyright © 2005 Deaconescu M. and Walls G. L.
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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 3, pp. 533–537, May–June, 2005.
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Deaconescu, M., Walls, G.L. On Orbits of Automorphism Groups. Sib Math J 46, 413–416 (2005). https://doi.org/10.1007/s11202-005-0044-8
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DOI: https://doi.org/10.1007/s11202-005-0044-8