QUESTION 3 Find the oder of the indicated element in indicated quotient group. a) 2 + (8)in Z12/ (8) b) 4 + (6> in Z12/ (6>
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- The elements of the multiplicative group G of 33 permutation matrices are given in Exercise 35 of section 3.1. Find the order of each element of the group. (Sec. 3.1,35) A permutation matrix is a matrix that can be obtained from an identity matrix In by interchanging the rows one or more times (that is, by permuting the rows). For n=3 the permutation matrices are I3 and the five matrices. (Sec. 3.3,22c,32c, Sec. 3.4,5, Sec. 4.2,6) P1=[ 100001010 ] P2=[ 010100001 ] P3=[ 010001100 ] P4=[ 001010100 ] P5=[ 001100010 ] Given that G={ I3,P1,P2,P3,P4,P5 } is a group of order 6 with respect to matrix multiplication, write out a multiplication table for G.Find two groups of order 6 that are not isomorphic.The alternating group A4 on 4 elements is the same as the group D4 of symmetries for a square. That is. A4=D4.