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(Solved): Consider An (to be the subgroup of Upper triangular matrices whose diagonal entries can be any n ...



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Consider (to be the subgroup of Upper triangular matrices whose diagonal entries can be any non zero elements from .) in (n by n matrices with non zero determinant and is finite field with p elements)). Let be the vector space of - valued function on (i.e these are functions from ) that are invariant with respect to left and right -translations. We introduce a binary operation on as follows. Given two bi invariant functions, define Consider with the convolution product. Denote the function which vanishes outside and equals 1 otherwise by . Let (resp. ) be subgroup in given by resp,. Denote the function which vanishes outside and equals 1 otherwise by , the characteristic function of is . Put and . We are given that the following relations hold. Prove that the elements generate


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