MATH 350 Final: MATH 350 Amherst F17M350 2801 29ZhangFinal

• School: Amherst College
• Department: Mathematics and Statistics
• Course: MATH 350
• Professor: All

Document Summary

Math 350-01 groups, rings and fields, fall 2017. December 19: (15 points) (a) (5 points) let g be a group and g a given element in g. prove that the function fg : g g de ned by x 7 gxg . 1 is an automorphism of g. (b) (5 points) the above fg is called an inner automorphism of g. let inn(g) be the set of all inner automorphisms of g. recall that (sg, ) is the symmetric group on. Show that (inn(g), ) is a subgroup of (sg, ). (c) (5 points) let z(g) be the center of g. prove that. Hint: use the fundamental theorem ( rst isomorphism theorem) on group homomor- phisms: (5 points) let g be a group and assume that h, k are subgroups of g such that |h| = 10 and |k| = 21.