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.
Dobson, T., Muzychuk, M., Spiga, P. (2022). Generalised dihedral CI-groups. ARS MATHEMATICA CONTEMPORANEA, 22(2), 2-7 [10.26493/1855-3974.2443.02e].
Generalised dihedral CI-groups
Spiga P.
2022
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.
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