Classification of Finite Simple Groups
نویسنده
چکیده
Analogous to the way the integers can be decomposed uniquely into prime factors, finite groups can be decomposed into finite simple groups, which cannot be further decomposed nontrivially. We will prove the JordanHölder Theorem and show that finite groups can always be decomposed uniquely into finite simple groups, and discuss the classification of these groups. In particular, we will discuss two infinite families of simple groups, the cyclic groups of prime order, and the alternating groups on n ≥ 5 elements.
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