Hostname: page-component-cb9f654ff-9b74x Total loading time: 0 Render date: 2025-08-20T04:05:03.712Z Has data issue: false hasContentIssue false
  • English
  • Français

On a new finite non–abelian simple group of Janko

Published online by Cambridge University Press:  17 April 2009

S. K. Wong
S. K. Wong
Affiliation:
Monash University, Clayton, Victoria.
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.

Two new simple groups have recently been discovered by Z. Janko. One of these groups has order 50,232,960. As a first step in showing that there is precisely one (up to isomorphism) simple group of order 50,232,960, the author proves in this paper the following result: If G is a non-abelian simple group of order 50,232,960, then the structure of the centralizer of an element of order two in G is uniquely determined.

In a note added on 21 April 1969 to this paper, the author announces that he has proved the uniqueness of the simple group of order 50,232,960.

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 1 , Issue 1 , April 1969 , pp. 59 - 79
Copyright
Copyright © Australian Mathematical Society 1969

References

[1] Brauer, Richard, “Investigations on group characters”, Ann. of Math. 42 (1941), 936–958.CrossRefGoogle Scholar
[2] Brauer, Richard, “On groups whose order contains a prime to the first power, I”, Amer. J. Math. 64 (1942), 401–420.CrossRefGoogle Scholar
[3] Brauer, Richard and Tuan, Hsio-Fu, “On simple groups of finite order, I”, Bull. Amer. Math. Soc. 51 (1945), 756–766.CrossRefGoogle Scholar
[4] Curtis, Charles W., Reiner, Irving, Representation theory of finite groups and associative algebras (Interscience, New York, London Sydney, 1962).Google Scholar
[5] Hall, Marshall Jr, The theory of groups (Macmillan, New York, 1959).Google Scholar
[6] Janko, Z., “Some new simple groups of finite order, I” (to appear).Google Scholar
[7] Stanton, R.G., “The Mathieu groups”, Canad. J. Math. 3 (1951), 164–174.CrossRefGoogle Scholar
[8] Suzuki, M., “Applications of group characters”, Proc. Sympos. Pure Math. (Amer. Math. Soc.) 1 (1959), 88–99.Google Scholar