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Published online by Cambridge University Press: 01 May 2003
Using the definition of regular p-group given by M. Hall [1], a new class of finite groups called regular-nilpotent has been defined. The action of these groups as automorphisms of compact Riemann surfaces has been investigated. It is proved that a necessary and sufficient condition for a Fuchsian group to cover a regular-nilpotent group is that its orbit genus be zero and its periods satisfy the least common multiple condition, first defined by Harvey [2] and Maclachlan [4].