Abstract
In the first part of this note, we give new proofs of known results regarding the class number of finite groups, adding a few related results. In the second part, we improve a result of Ito concerning a special class ofp-groups.
Similar content being viewed by others
References
P. Hall,The Eulerian functions of a group, Quart. J. Math.7 (1936), 134–151.
K. A. Hirsch,On a theorem of Burnside, Quart. J. Math (2)1 (1950), 97–99.
G. T. Hogan and W. P. Kappe,On the H p -problem for finite p-groups, Proc. Amer. Math. Soc.20 (1969), 450–454.
B. Huppert,Endliche Gruppen I, Berlin, 1967.
N. Ito,On finite groups with given conjugate types I, Nagoya. Math. J.6 (1953), 17–28.
M. Konvisser and D. Jonah,Counting abelian subgroups of p-groups. A projective approach, J. Algebra34 (1975), 309–330.
J. Poland,Two problems on finite groups with k conjugate classes, J. Austral. Math. Soc.8 (1968), 49–55.
J. Rebmann,F-Gruppen, Arch. Math.22 (1971), 225–230.
D. M. Rocke,p-groups with abelian centralizers, Proc. London Math. Soc. (3)30 (1975), 55–75.
R. W. van der Waall,On a theorem of Burnside, Elem. Math.25 (1970), 136–137.
W. Feit,Characters of Finite Groups, New York, 1967.
W. Burnside,Theory of Groups of Finite Order, 2nd ed., Dover, 1955.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Mann, A. Conjugacy classes in finite groups. Israel J. Math. 31, 78–84 (1978). https://doi.org/10.1007/BF02761381
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02761381