Abstract
Given a construction f on groups, we say that a group G is f -realisable if there is a group H such that G ≅ f ( H ) , and completely f-realisable if there is a group H such that G ≅ f ( H ) and every subgroup of G is isomorphic to f ( H 1 ) for some subgroup H 1 of H and vice versa. Denote by L ( G ) the absolute center of a group G, that is the set of elements of G fixed by all automorphisms of G. By using the structure of the automorphism group of a ZM-group, in this paper we prove that cyclic groups C N , N ∈ N * , are completely L-realisable.
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