Abstract
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 an ecessary 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 ,fi rst defined by Harvey (2 )a nd Maclachlan (4).
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