Difference between revisions of "Abelian Group"

Line 23: Line 23:
 
!a
 
!a
 
|a|e|b|b
 
|a|e|b|b
−
}
+
|}
 
_____________________
 
_____________________
 
|___|_e_|_a_|_b_|_c_|
 
|___|_e_|_a_|_b_|_c_|

Revision as of 21:38, 9 December 2013

Let <math>G{e,a,b,c}</math> be an abelian group with <math>'e'</math> as an identity element. The order of the other elements are:

(A)2,2,3

(B)3,3,3

(C)2,2,4

(D)2,3,4

Solution

e a b c
e a|b|c
a e|b|b

_____________________ |___|_e_|_a_|_b_|_c_| |_e_|_e_|_a_|_b_|_c_| |_a_|_a_|_e_|_b_|_b_| |_b_|_b_|_c_|_e_|_e_| |_c_|_c_|_b_|_e_|_a_|

Retrieved from "https://gatecse.in/w/index.php?title=Abelian_Group&oldid=1369"

Let <math>G{e,a,b,c}</math> be an abelian group with <math>'e'</math> as an identity element. The order of the other elements are:

(A)2,2,3

(B)3,3,3

(C)2,2,4

(D)2,3,4

Solution[edit]

e a b c
e a|b|c
a e|b|b

_____________________ |___|_e_|_a_|_b_|_c_| |_e_|_e_|_a_|_b_|_c_| |_a_|_a_|_e_|_b_|_b_| |_b_|_b_|_c_|_e_|_e_| |_c_|_c_|_b_|_e_|_a_|