2. HOMOMORPHISMS AND SUBGROUPS 33 Theorem 2.8. If G is a group and X is a nonempty subset of G, then the subgroup (X) ge

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2 Homomorphisms And Subgroups 33 Theorem 2 8 If G Is A Group And X Is A Nonempty Subset Of G Then The Subgroup X Ge 1 (17.89 KiB) Viewed 63 times

2. HOMOMORPHISMS AND SUBGROUPS 33 Theorem 2.8. If G is a group and X is a nonempty subset of G, then the subgroup (X) generated by X consists of all finite products a "a,m...a"(a; eX;n; € Z). In particular for every a e G, (a) = (a" | nez.