MATH 113 Study Guide - Quiz Guide: Brie
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Please write your name and sid at the top right. This quiz is out of 25 points: (10 points) let g be a group, h g a subgroup, and g an element of g (not necessarily in h). Prove using the de nition that s is a subgroup of g . H since h is a subgroup. (closure under inversion) let ghg 1 be in s. Its inverse is (g 1) 1h 1g 1 = gh 1g 1, which is in s as h 1 is in h, since h h and h is a subgroup: (2 points each) true or false. You don"t need to explain your answer. (a) in d8, every element has order 1, 2, or 4. True. (b) if h is a subgroup of an in nite group g , then there are in nitely many left h-cosets. If it"s p, then (cid:104)g(cid:105) is the desired subgroup.
