3. Let G be a group of order 3 and identity e. If the other elements are a and b, use the Latin square property to draw up the group table for G, and deduce that a3 = e
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- Find two groups of order 6 that are not isomorphic.45. Let . Prove or disprove that is a group with respect to the operation of intersection. (Sec. )Cs.google.com/forms/d/e/1FAlpQLSdMsXFXAUuUIOLJrrhM9uiYZRdcxMxgBHHj4ddS9x_Do4b6qA/formResponse The following is a Cayley table for a group G. The order of 3 is: 2 2 4 1 2 3 4 4 1 2 4 4. 3 4 5 2 O 4 EN ere to search TOSHIBA SE23 451234 512
- Let a be an element of order 8 in a group G. Then order of a Select one: а. 6 b. 48 С. 2 d. 4Let G be a group of order 3 and identity e. If the other elements are a and b, use the Latin squareproperty to draw up the group table for G, and deduce that a3 = eWrite down the six elements of S3 and give the multiplication table for the group. The six elements of S3 are then: 2 2 2 3 1 = (1/²/3) a = (2²2 ² 3). b = (² ² 2) 2 3 1 3 1 1 1 2 c = (²2²3). d= (² 2 3). e= (1 ² 3) C 1 3 1 3 The multiplication table for S3 can be written down directly by doing the required composition. Find ab, de,and c^2 1 2 1 2 1 2 2 3 a = (2²2 ²7 ³3) a = ( 2² ²3 ³ ) = b (² ² 2) ²= ( 2₂ ²3 ³) a= 3 1 1 3 1 1. = (1 2² ₂3 ) = 1 2 1 2 2 1 c = ( ²2 ²3 ) c = ( 2₂ ²3 ) = c ² = c = (₁ ²²3) ²¹ C C 1 1 2 3. a3 =