MAT 150A Study Guide - Final Guide: Normal Subgroup
1 May 2019
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G- group g1, g2 g st g1, g2 have nite order but g1g2 has in nite order. If g1g2 = g2g1 then g1g2 has nite order provided both g1, g2 have. Homework: show that the composition of two re ections is a rotation about the origin with angle 2( 1 2) assume we measure in degrees and 2( 2 1) is irrational. Find all integers x, s (g1g2)(cid:20)1 sin(2n( 2 1))(cid:21) 0(cid:21) = (cid:20)cos(2n( 2 1)) when multiple of pi. Crt x 2 mod 3 x 1 mod 4 x 3 mod 5. By the crt, a solution should exist (1), 4, 1, 2, 5, 8, 11, 14, 1729 (1&2)5, 17, 29, 41, 53 (1&2&3) 7, 53, 113, 173, 233. Show that an sn is a normal subgroup. [sn : an] = 2 = an is normal in sn. Then the following are equivalent: h is normal, a g ah = ha, a g, b g st ah = hb.
