mersenneforum.org  

Go Back   mersenneforum.org > Extra Stuff > Miscellaneous Math

Reply
 
Thread Tools
Old 2004-11-28, 05:04   #1
devarajkandadai
 
devarajkandadai's Avatar
 
May 2004

31610 Posts
Default 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
devarajkandadai is offline   Reply With Quote
Old 2004-12-03, 07:07   #2
devarajkandadai
 
devarajkandadai's Avatar
 
May 2004

22×79 Posts
Default 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
devarajkandadai is offline   Reply With Quote
Old 2004-12-03, 11:54   #3
dave_0273
 
dave_0273's Avatar
 
Oct 2003
Australia, Brisbane

2×5×47 Posts
Default

Would you mind please doing a numerical example please??
dave_0273 is offline   Reply With Quote
Old 2004-12-06, 05:32   #4
devarajkandadai
 
devarajkandadai's Avatar
 
May 2004

22×79 Posts
Default 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.
A.K. Devaraj
devarajkandadai is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
MaximumPC geek quiz... kracker Lounge 14 2014-05-13 14:33
Problem with quiz kemik Homework Help 27 2005-06-16 11:53
English Quiz. mfgoode Lounge 16 2005-04-04 16:21
Maths Quiz-I devarajkandadai Miscellaneous Math 8 2004-11-22 04:48
MATHS MUSINGS -I-Maths & Teaching Kung-Fu devarajkandadai Miscellaneous Math 0 2004-09-16 04:27

All times are UTC. The time now is 01:28.


Wed Oct 27 01:28:22 UTC 2021 up 95 days, 19:57, 0 users, load averages: 1.28, 1.27, 1.25

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2021, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.