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Let a = (1 2 3 4 5 3 4 5 2 1) and b =(1 2 3 4 5 5 3 2 4 1) in S7. Write ab as a product of disjoint permutations. Further, is ab even? Why, or why not?
Is R = {[a a+b a+b b ] |a,b belongs to Z} a subring of M2(Z)? Why or why not?
Let a = (3 4 5 2 1) and b = (5 3 2 4 1) in S7. Write ab as a product of disjoint permutations. Further, is ab even? Why or why not?
Find the permutation in S_4​such that 1→3, 2 2→1, 3→2.
There are the permutations σ=(123), τ=(12). Calculate σ(τ)=τσ (applying \tauτ first and then applying \sigmaσ) Find the order of the element 2in the group (Z_6,+) Find the element which belongs to the ring Z_2[x] /x^2+x+1 Let the order of element aa in the finite group be 20. Find the order of element a^6 ​
Find the permutation in S_4 ​ such that 1→3, 2 12→1, 23→2.
Calculate 2+2 in Z_3 ​
modules which are neither Noetherian nor Artinian.is it true of false.if it is one them then give proof
Why zero ring is artinian as well as noetherian?
A Minimal Sub-Module is always Simple ?
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