MAT-3110 Midterm: MATH 3110 App State Spring2009 Test3
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The last page is a copy of cayley tables for d3 and d4. The tables should be helpful when doing problems 3 and 4. Why or why not? (b) recall a4 = {(1), (123), (132), (124), (142), (134), (143), (234), (243), (12)(34), (13)(24), (14)(23)}. Show a4 6 = d6 (they are not isomorphic). Hint: think about orders of elements. (c) g is a group of order 5. /20 points) homomorphisms (a) let g = (cid:26)(cid:20)1 a. 0 a r(cid:27) and let : g r be de ned by (cid:18)(cid:20)1 a. 0 homomorphism and nd the kernel of . /20 points) write down the left multiplication operators for d3 and translate them into per- 3, b 4, ab 5, a2b 6. muations (in s6) labeling the elements of d3 as follows: 1 1, a 2, a2. Write down a subgroup of s6 which isomorphic to d3 (using cayley"s theorem).
