Centralizers and conjugacy. Let G be a group. For any element a EG, the centralizer Ca of a is the set of all elements which commute with a: Ca = {x € G: xa = ax} = {x € G:a= xax1}. (1) Show that Ca is a subgroup of G. (2) Show that xax-1 = yay-1 if and only if xCa =yCa. (3) Show that the conjugates of a are in bijective correspondence with the left cosets of Ca. Thus if G is finite, the conjugacy class [a] has [G: Ca] elements, and the size of the conjugacy class divides the order of the group. (4) Let p be prime and let G be a group of order pa for some a > 1. Recall that the center of G is C(G) = {a EG: ax = xa for all x EG}. Show that C(G) + {e}. (Hint: Use problem

y/x=18

step-by-step explanation:

connie < felicia < stew

step-by-step explanation:

stew:

we need to find the slope

m = (y2-y1)/ (x2-x1)

    = (2650-795)/(10-3)

    = 1855/7

265 words per minute

connie:

we need to find the slope

m = (y2-y1)/ (x2-x1)

we have two points (0,0) and (4,800)

m = (800-0)/(4-0)

  m = 800/4

    200 words per minute

felicia:

260 words per minute

200< 260 < 265

connie < felicia < stew

  y= -3x is the required function.

step-by-step explanation:

we have been given a table:

x             y

0             0

1             -3

3             -9

-2             6

we can see that the values of y is -3 times the value of x

hence, the function would be: y= -3x.

put the values of x will give the same y as in the table that means function is satisfying the given table.

step-by-step explanation:

1. practice, practice & more practice

2. review errors

3. master the key concepts

do not try to memorise the processes.

4. understand your doubts.

5. create a distraction free study environment

6. create a mathematical dictionary

7. apply maths to real world problems.