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arXiv · 1305.5974

Introduction to Sporadic Groups for physicists

Luis J. Boya
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Abstract

We describe the collection of finite simple groups, with a view on physical applications. We recall first the prime cyclic groups $Z_p$, and the alternating groups $Alt_{n>4}$. After a quick revision of finite fields $\mathbb{F}_q$, $q = p^f$, with $p$ prime, we consider the 16 families of finite simple groups of Lie type. There are also 26 \emph{extra} "sporadic" groups, which gather in three interconnected "generations" (with 5+7+8 groups) plus the Pariah groups (6). We point out a couple of physical applications, including constructing the biggest sporadic group, the "Monster" group, with close to $10^{54}$ elements from arguments of physics, and also the relation of some Mathieu groups with compactification in string and M-theory.

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Luis J. Boya. 2013-05-25. Introduction to Sporadic Groups for physicists. https://doi.org/10.1088/1751-8113%2F46%2F13%2F133001

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