ALL SIMPLE GROUPS WITH ORDER FROM 1 MILLION TO 5 MILLION ARE EFFICIENT

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CAMPBELL COLIN M.; HAVAS GEORGE; RAMSAY COLIN; ROBERTSON EDMUND F.

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Journal Paper

Paper Information

Journal: INTERNATIONAL JOURNAL OF GROUP THEORY Year:2014 | Volume:3 | Issue:1 Page(s): 17-30

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Information Journal Paper

Title

ALL SIMPLE GROUPS WITH ORDER FROM 1 MILLION TO 5 MILLION ARE EFFICIENT

Author(s)

CAMPBELL COLIN M. | HAVAS GEORGE | RAMSAY COLIN | ROBERTSON EDMUND F. | Issue Writer Certificate

Keywords

EFFICIENT PRESENTATIONS

SIMPLE GROUPS

COSET ENUMERATION

Abstract

There is much interest in finding short presentations for the finite SIMPLE GROUPS. Indeed it has been suggested that all these groups are efficient in a technical sense. In previous papers we produced nice EFFICIENT PRESENTATIONS for all except one of the SIMPLE GROUPS with order less than one million. Here we show that all SIMPLE GROUPS with order between 1 million and 5 million are efficient by giving EFFICIENT PRESENTATIONS for all of them. Apart from some linear groups these results are all new. We also show that some covering groups and some larger SIMPLE GROUPS are efficient. We make substantial use of systems for computational group theory and, in particular, of computer implementations of COSET ENUMERATION to find and verify our presentations.

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APA: Copy

CAMPBELL, COLIN M., HAVAS, GEORGE, RAMSAY, COLIN, & ROBERTSON, EDMUND F.. (2014). ALL SIMPLE GROUPS WITH ORDER FROM 1 MILLION TO 5 MILLION ARE EFFICIENT. INTERNATIONAL JOURNAL OF GROUP THEORY, 3(1), 17-30. SID. https://sid.ir/paper/595809/en

Vancouver: Copy

CAMPBELL COLIN M., HAVAS GEORGE, RAMSAY COLIN, ROBERTSON EDMUND F.. ALL SIMPLE GROUPS WITH ORDER FROM 1 MILLION TO 5 MILLION ARE EFFICIENT. INTERNATIONAL JOURNAL OF GROUP THEORY[Internet]. 2014;3(1):17-30. Available from: https://sid.ir/paper/595809/en

IEEE: Copy

COLIN M. CAMPBELL, GEORGE HAVAS, COLIN RAMSAY, and EDMUND F. ROBERTSON, “ALL SIMPLE GROUPS WITH ORDER FROM 1 MILLION TO 5 MILLION ARE EFFICIENT,” INTERNATIONAL JOURNAL OF GROUP THEORY, vol. 3, no. 1, pp. 17–30, 2014, [Online]. Available: https://sid.ir/paper/595809/en

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