Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-27T15:50:59.986Z Has data issue: false hasContentIssue false
  • English
  • Français

CONJUGACY CLASS SIZES IN FINITE GROUPS

Part of: Representation theory of groups Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  01 October 2008

AVINOAM MANN
AVINOAM MANN*
Affiliation:
Einstein Institute of Mathematics, Hebrew University, Jerusalem, Israel (email: [email protected])
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We make several conjectures, and prove some results, pertaining to conjugacy classes of a given size in finite groups, especially in p-groups and 2-groups.

Keywords

conjugacy classesp-groups2-groups

MSC classification

Secondary: 20D15: Nilpotent groups, $p$-groups 20E45: Conjugacy classes
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 85 , Issue 2 , October 2008 , pp. 251 - 255
Copyright
Copyright © 2008 Australian Mathematical Society

References

[1]Barnea, Yiftach and Isaacs, I. M., ‘Lie algebras with few centralizer dimensions’, J. Algebra 259 (2003), 284–299.Google Scholar
[2]Camina, Alan R., ‘Finite groups of conjugate rank 2’, Nagoya Math. J. 53 (1974), 47–57.Google Scholar
[3]Huppert, Bertram, Endliche Gruppen I (Springer, Berlin, 1967).Google Scholar
[4]Ishikawa, Kenta, ‘On finite p-groups which have only two conjugacy lengths’, Israel J. Math. 129 (2002), 119–123.Google Scholar
[5]Isaacs, I. M., ‘Groups with many equal classes’, Duke Math. J. 37 (1970), 501–506.Google Scholar
[6]Isaacs, I. M., ‘Subgroups generated by small classes in finite groups’, Proc. Amer. Math. Soc. 136 (2008), 2299–2301.Google Scholar
[7]Ito, Noboru, ‘On finite groups with given conjugate types. I’, Nagoya Math. J. 6 (1953), 17–28.Google Scholar
[8]Ito, Noboru, ‘On finite groups with given conjugate types. II’, Osaka J. Math. 7 (1970), 231–251.Google Scholar
[9]Ito, Noboru, ‘On finite groups with given conjugate types. III’, Math. Z. 117 (1970), 267–271.Google Scholar
[10]Ito, Noboru, ‘Simple groups of conjugate type rank 4’, J. Algebra 20 (1972), 226–249.Google Scholar
[11]Ito, Noboru, ‘Simple groups of conjugate type rank 5’, J. Math. Kyoto Univ. 13 (1973), 171–190.Google Scholar
[12]Ito, Noboru and Mann, Avinoam, ‘Counting classes and characters of groups of prime exponent’, Israel J. Math. 156 (2006), 205–220.Google Scholar
[13]Keller, T. M., Ragan, D. and Tims, G. T., ‘The Taketa bound for normally monomial p-groups of maximal class’, J. Algebra 277 (2004), 675–688.Google Scholar
[14]Mann, Avinoam, ‘Conjugacy classes in finite groups’, Israel J. Math. 31 (1978), 78–84.Google Scholar
[15]Mann, Avinoam, ‘Groups with few class sizes and the centraliser equality subgroup’, Israel J. Math. 142 (2004), 367–380.Google Scholar
[16]Mann, Avinoam, ‘Elements of minimal breadth in finite p-groups and Lie algebras’, J. Austral. Math. Soc. 81 (2006), 209–214.Google Scholar
[17]Rebmann, Jochen, ‘F-Gruppen’, Arch. Math. 22 (1971), 225–230.CrossRefGoogle Scholar
[18]Verardi, Libero, ‘On groups whose non-central elements have the same finite number of conjugates’, Boll. Unione Mat. Ital. (7) 2-A (1988), 391–400.Google Scholar