Which of the following is not a group? a.(Z, x) b.(N, +) c. (R, x), only a, only c, only b, a, b and c, How many identity elements are there in a group?, 1, 2, nil, 3, The identity element of the group (Z, *) where a*b = a+b+1 is, -1, 1, 2, 0, If H and K are two subgroups of a group G then which of the following is a subgroup of G?, HUK, H⋂K, HK, None, If o(a) = n, a∈G, then am = e if, n∤ m ( n does not divide m), m ∣ n ( m divides n), mn = e, n ∣ m ( n divides m), If a is an element of a group (G *) such that a*a = e then a-1 =, e, 1/a, a, none, Which of the following is a group?, set of integers w.r.t multiplication, set of integers w.r.t addition, set of rational numbers w.r.t multiplication, none, the generators of the cyclic group {1,⍵,⍵2} w.r.t multiplication are, 1, ⍵, 1, ⍵2, ⍵, ⍵2, none, A group (G *) is said to be abelian if * is, associative and commutative, associative, commutative, none, In the set of rational number Q, * is defined by a*b = a+b - ab. The inverse of a is, a/(a - 1), a/ (1 - b), 1 - a, none

Groups, Subgroups

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