On power endomorphisms of n-central groups

Primož Moravec 1 , 1
  • 1 Institute of Mathematics, Physics and Mechanics, Jadranska 19, 1000 Ljubljana, Slovenia.


A group G is said to be n-central if the factor group G/Z(G) is of exponent n. We improve a result of Gupta and Rhemtulla by showing that every 4-central group is 16-abelian and every 6-central group is 36-abelian. There are examples of finite groups which show that these bounds are best possible. Consequently, we can completely describe the structure of exponent semigroups of free non-cyclic n-central groups for n = 2, 3, 4, 6. We obtain a characterization of metabelian p-central groups and a classification of finitely generated 2-central groups. We compute the nilpotency class of the free metabelian 4-central group of arbitrary finite rank.

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The Journal of Group Theory is devoted to the publication of original research articles in all aspects of group theory. Articles concerning applications of group theory and articles from research areas which have a significant impact on group theory will also be considered.