 mersenneforum.org Maths Quiz-II
 Register FAQ Search Today's Posts Mark Forums Read 2004-11-28, 05:04 #1 devarajkandadai   May 2004 31610 Posts Maths Quiz-II __A Small Problem In Group Theory Let T(a,b) be the function ax + b. T(a,b) is a group with identity = T(1,0) and product given by T(a,b).T(c,d) = T(ac,ad + b) Now let m and n be fixed values of a and b respectively. Problem: To derive an expression in a,b, m and n which will generate a Normal subgroup of T(a,b). A.K. Devaraj   2004-12-03, 07:07   #2

May 2004

22×79 Posts Maths Quiz II

Quote:
 Originally Posted by devarajkandadai __A Small Problem In Group Theory Let T(a,b) be the function ax + b. T(a,b) is a group with identity = T(1,0) and product given by T(a,b).T(c,d) = T(ac,ad + b) Now let m and n be fixed values of a and b respectively. Problem: To derive an expression in a,b, m and n which will generate a Normal subgroup of T(a,b). A.K. Devaraj
Put b/(a-1) = n/(m-1)

You will now get a Normal Subgroup of the given group.In case this is not
clear I wd be only too happy to illustrate with a numerical example.
A.K. Devaraj   2004-12-03, 11:54 #3 dave_0273   Oct 2003 Australia, Brisbane 2×5×47 Posts Would you mind please doing a numerical example please??   2004-12-06, 05:32   #4

May 2004

22×79 Posts Maths Quiz II

Quote:
 Originally Posted by dave_0273 Would you mind please doing a numerical example please??
Let m = 7 and n = 12

b/(a-1) = n/(m-1) = 2.

Now let a = 3; then b = 4

Hence we have to test whether T(3,4) is a member of the relevant
Normal subgroup.Recall if N is a normal subgroup then

g^(-1)Ng should be = N.

Carrying out thi s test w.r. t. g = T(7,12) and N = T(3,4) is successful.

Trust this is clear.
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