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FINITE GROUPS WHOSE NONCENTRAL COMMUTING ELEMENTS HAVE CENTRALIZERS OF EQUAL SIZE.
- Source :
-
Bulletin of the Australian Mathematical Society . Oct2010, Vol. 82 Issue 2, p293-304. 12p. - Publication Year :
- 2010
-
Abstract
- A finite group is called a CH-group if for every x, y ϵ G\Z(G), xy = yx implies that ∥CG(x)∥ = ∥CG(y)∥. Applying results of Schmidt ['Zentralisatorverbände endlicher Gruppen', Rend. Sem. Mat. Univ. Padova 44 (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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00049727
- Volume :
- 82
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Bulletin of the Australian Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 53529131
- Full Text :
- https://doi.org/10.1017/S0004972710000298