Finite groups with exactly two conjugacy classes of the same order

Authors
Boner, CM Ward, MB
Citation
Cm. Boner et Mb. Ward, Finite groups with exactly two conjugacy classes of the same order, R MT J MATH, 31(2), 2001, pp. 401-416
Citations number
10
Categorie Soggetti
Mathematics
Journal title
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS
ISSN journal
00357596 → ACNP
Volume
31
Issue
2
Year of publication
2001
Pages
401 - 416
Database
ISI
SICI code
0035-7596(200122)31:2<401:FGWETC>2.0.ZU;2-F
Abstract
We show that the only finite groups having a nilpotent derived subgroup and having exactly two conjugacy classes of the same order are Z(2), D-10, the dihedral group of order 10, and A(4). As a corollary, the only supersolvab le finite groups having exactly two conjugacy classes of the same order are Z(2) and D-10.