Harada-Norton group

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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.

[edit] 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.
• Atlas of Finite Group Representations: Harada-Norton group

[edit] External links

• MathWorld: Harada-Norton Group