Unformatted text preview: GL (2 , Z 2 ) represent the group of 2 × 2 matrices with coeFcients in Z 2 and determinant 1 (calculated mod 2). What is the cardinality n of this group? List its elements. Write out its multiplication table. Identify the group with a subgroup of S ( n ) (as usual, thinking of each element as de²ning, by leftmultiplication, a permutation of the elements of the group). Is this a group we have seen before, perhaps in di³erent clothing? Hint: consider the action by leftmultiplication of GL (2 , Z 2 ) on the column vectors 1 = p 1 P , 2 = p 1 P , 3 = p 1 1 P . 6. In the permutation group S (4), let H represent the subgroup H = { e, (1234) , (13)(24) , (1432) } . H should have 6 left cosets. What are they? Describe them by listing their elements. 1...
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 Fall '10
 AnthonyPhillips
 Subgroup, linear fractional transformation, linear fractional transformations

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