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Original Articles

Exact Factorizations of Sporadic Simple Groups

 

Abstract

A group G is said to have an exact factorization if there exist proper subgroups Ai for i=1,2,,n such that G=A1A2An and |G|=|A1||A2||An|. The number n is called length of this factorization. An exact factorization of length 3 is called exact triple factorization. In this article, we show the existence of exact factorizations of seven sporadic simple groups J1,J2,HS,McL,He,Ru and Co3. Our factorizations for five groups are exact triple. There are no reported factorizations for the groups J1,McL and Co3. We will present an exact triple factorization for Co3 and exact factorizations for J1 and McL of length four.

2010 AMS SUBJECT CLASSIFICATION:

Acknowledgment

I would like to thank the anonymous referee who read the paper carefully and proposed corrections.

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