Test: Group Theory - 3

Set (1,2,3,4} is a finite abelian group of order... under multiplication modulo ... as composition.

Let G be a group of order 7 and φ(x) = x⁴, x ∈ G. Then f is 

HK is a sub-group of G iff

Check the correct statement.

If a, b ∈ G, a group, then b is conjugate to a, if there exist c ∈ G, such that

If H₁ and H₂ are two subgroups of G, then following is also a subgroups of G

If (G, *) is a group and for all a, b ∈ G, b^-1 * a^-1* b * a = e, then G is

Number of elements of the cyclic group of order 6 can be used as generators of the group are

The multiplicative group {1, -1} is a subgroup of the multiplicative group

A set G with a binary composition denoted multiplicative is a group, if

In the additive group of integers, the order of every elements a ≠  0 is

Let Z be a set of integers, then under ordinary multiplication (Z, ·) is

Set of all n, nth roots of unity from a finite abelian group of order n with respect to

The generators of a group G = {a, a², a³, a⁴, a⁵, a⁶ = e) are

If G is a group such that a2 = e, for all a ∈ G, then G is

Consider the system of equations x + y + z = 1, 2x + 3y + 2z = 1, 2x + 3y + (a^{2 – 1})z = a + 1 then

If G is a group, then for all a, b ∈ G