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Working on Finite Permutation Groups:  Let f = (1 6)(2 3 5 4), Find f103 and f-2.

Working on Finite Permutation Groups:  Let f = (1 6)(2 3 5 4), Find f103 and f-2.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Working on Finite Permutation Groups: 

Let f = (1 6)(2 3 5 4), Find f103 and f-2.

Expert Solution
Step 1

Here. f= (1 6)(2 3 5 4)

Since order of (1 6) =2 & order of (2 3 5 4)=4

we know. order of f =l.c.m of order of (1 6) & order of 4

                                =l.c.m {2,4}

                                =4

this implies f4=I

Now, (f4)25=(I)25

      ⇒f100=I

  f103=f100f3=f3I

                        =f3

Now,  f3=(1 6)3(2 3 5 4)3

               =(1 6)( 2 4 5 3)         (as to find cube of permutation by shortcut, we leave2 digits in between)

so, f103=(1 6)( 2 4 5 3)

                                                  

 

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