Question

1. A Cayley diagram and multiplication table for the dihedral group Ds are shown below Section 2 of the class lecture notes describes two algorithms for expressing a group G of order n as a set of permutations in Sn. One algorithm uses the Cayley diagram and the other uses the multiplication table. In this problem, you will explore this a bit further. (a) Label the vertices of the Cayley diagram from the set (1,... ,8) and use this to construct a permutation group isomorphic to Ds, and sitting inside Ss (b) Label the entries of the multiplication table from the set (1,...,8) and use this to construct a permutation group isomorphic to D4, and sitting inside Ss (c) Are the two groups you got in Parts (a) and (b) the same? (The answer will depend on your choice of labeling.) If "yes", then repeat Part (a) with a different labeling to yield a different group. If "no", then repeat Part (a) with a different labeling to yield the group you got in Part (b) 2. Find all subgroups of the following groups, and arrauge them in a Hasse diagram, or

Answer 1

https://math.stackexchange.com/questions/146923/is-the-cayley-diagram-for-d4-in-wikimedia-commons-wring

3 3 3 (3) both are same For diffevent conside