FINITE GROUPS WHOSE NONCENTRAL COMMUTING ELEMENTS HAVE CENTRALIZERS OF EQUAL SIZE

Author:

DOLFI SILVIO,HERZOG MARCEL,JABARA ENRICO

Abstract

AbstractA finite group is called a CH-group if for every x,yGZ(G), xy=yx implies that $\|\cent Gx\| = \|\cent Gy\|$. Applying results of Schmidt [‘Zentralisatorverbände endlicher Gruppen’, Rend. Sem. Mat. Univ. Padova44 (1970), 97–131] and Rebmann [‘F-Gruppen’, Arch. Math. 22 (1971), 225–230] concerning CA-groups and F-groups, the structure of CH-groups is determined, up to that of CH-groups of prime-power order. Upper bounds are found for the derived length of nilpotent and solvable CH-groups.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference11 articles.

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