Generalized dihedral CI-groups

Ted Dobson, Mikhail Muzychuk, Pablo Spiga

Abstract


In this paper, we find a strong new restriction on the structure of CI-groups. We show that, if R is a generalised dihedral group and if R is a CI-group, then for every odd prime p the Sylow p-subgroup of R has order p, or 9. Consequently, any CI-group with quotient a generalised dihedral group has the same restriction, that for every odd prime p the Sylow p-subgroup of the group has order p, or 9.


Keywords


CI-group, DCI-group, generalised dihedral, Cayley isomorphism

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DOI: https://doi.org/10.26493/1855-3974.2443.02e

ISSN: 1855-3974

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