show that the set Z ={0,+-1, +-2,...} with the operation of multiplication (a,b) map to ab is not a group Show that the operation (a,b) map to a*b =ab on the set of positive real numbers is not associative. for the permutation sigma belongs to S8 sigma=(3 7 4 2 6 8 1 5). Find the number of inversions I(sigma) sgn sigma =(-1)sigma , the decomposition into a product of independent cycles and the order
show that the set Z ={0,+-1, +-2,...} with the operation of multiplication (a,b) map to ab is not a group
Show that the operation (a,b) map to a*b =ab on the set of positive real numbers is not associative.
for the permutation sigma belongs to S8 sigma=(3 7 4 2 6 8 1 5). Find the number of inversions I(sigma) sgn sigma =(-1)sigma , the decomposition into a product of independent cycles and the order
for the permutation sigma belongs to S8 tau=(7 4 8 1 3 5 6 2). Find the number of inversions I(sigma) sgn sigma =(-1)sigma , the decomposition into a product of independent cycles and the order
find the permutation U belongs to S8 such that sigma *U = tau
where sigma=(3 7 4 2 6 8 1 5), tau=(7 4 8 1 3 5 6 2) are the permutation. decompose U into product of indepent cycles, find the sign and order
consider the group of permutations Sn. Let A={a1,..., ak} subset of {1; : : : ; n}be a set of k less than equal to n distinct elements. Let SA subset of Sn be the set of permutationspreserving the setA, that is, permutations sigma such that for everyi= 1; : : : ; k we have sigma(ai) =aj for some j belongs to{1; : : : ; k}(depending on i).
(i) Prove that SA a group with respect to the operation of taking the usualcomposition of permutations.(ii) Find the number of elements inSA
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