Harada-Norton group

Harada-Norton group

In the mathematical field of group theory, the Harada-Norton group "HN" (found by Koichiro Harada (1975) and Simon Norton (1975)) is a sporadic simple group of order

: 214 · 36 · 56 · 7 · 11 · 19 : = 273030912000000: ≈ 3 · 1014.

The prime 5 plays a special role in the group. For example, it centralizes an element of order 5 in the Monster group, and as a result acts naturally on a vertex operator algebra over the field with 5 elements.

References

*K. Harada, "On the simple group F of order" 214 · 36 · 56 · 7 · 11 · 19, proceedings of the conference on finite groups, (Utah 1975), edited by Scot and Gross, Academic press 1976.
*S. P. Norton, "F and other simple groups", PhD Thesis, Cambridge 1975.
* [http://brauer.maths.qmul.ac.uk/Atlas/v3/spor/HN/ Atlas of Finite Group Representations: Harada-Norton group]

External links

* [http://mathworld.wolfram.com/Harada-NortonGroup.html MathWorld: Harada-Norton Group]


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