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Simple Groups and Sylow p-Subgroups

(1) Prove that if |G|=1365, then G is not simple.

(2) Assume that G is a nonabelian group of order 15. Prove that Z(G)=1. Use the fact that the group generated by "g" is less than or equal to C_G(g) for all "g" in G to show that there is at most one possible class equation for G.

Solution Summary

Simple Groups and Sylow p-Subgroups are investigated.

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