In Section 9E we proved the abstract Fermat theorem: if G is an abelian group with n elements, then a n = e for any a in G. In this section we will show that if H is any subgroup of G, then the number of elements of H is a divisor of the number of elements of G. This famous result is called Lagrange’s theorem. Euler’s and Fermat’s theorems are easy consequences of Lagrange’s theorem.
KeywordsFinite Group Identity Element Group Homomorphism Rigid Motion Ring Homomorphism
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