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FINITE GROUPS WHOSE NONCENTRAL COMMUTING ELEMENTS HAVE CENTRALIZERS OF EQUAL SIZE
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 82 / Issue 2 / October 2010
- Published online by Cambridge University Press:
- 07 July 2010, pp. 293-304
- Print publication:
- October 2010
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- Article
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A finite group is called a CH-group if for every x,y∈G∖Z(G), xy=yx implies that
. 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.
. Applying results of Schmidt [‘Zentralisatorverbände endlicher Gruppen’, 