This preview shows page 1. Sign up to view the full content.
Unformatted text preview: Kra.) 5. Let 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 dening, by leftmultiplication, a permutation of the elements of the group). Is this a group we have seen before, perhaps in dierent clothing? 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...
View
Full
Document
 Fall '08
 Staff

Click to edit the document details