# Group Theory

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Lets S1 and S2 be two algebric structure :

S1 : {0,1,2,3,4,….,m-1},+m-1

S2 : {0,1,2,3,4,….,m-2},+m-1

+m is the addition modulo m. Which of the following are Groups ?
0
I get it for S2, but little confused why S1 IS WRONG ?
1
consider S1={0,1,2,3} on addition mudulo 3

then you can check that identity element does not exist

0 (addition mpdulo 3) 3 is 0 here...not 3

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