Test: Group Theory - 5 - Mathematics MCQ

Suppose K_m = {P∈S_m|, |P| is odd prime}. Determine the set for which m ≥ 3 Km a subgroup of Sm.

If a ∈ G is of order n and P is prime to n, then the order of a^P is

The generators of the group G = {a, a², a³, a⁴ = e} are

If order of group G is P², where P is prime, then

A relation (34 × 78) × 57 = 34 × (78 × 57) can have __________ property.

The inverse of an odd permutation is

Let R be the ring of all 2 × 2 matrices with integer entries. Which of the following subsets of R is an integral domain?

Statement: All cyclic groups are abelian. Statement B: The order of cyclic group is same as the order of its generator.

If f = (2 3) and g = (4 5) be two permutation on five symbols 1, 2, 3,4, 5 then gf is

The permutation  is equal to

Statement A : Every isomorphic image of a cyclic group is cyclic.
Statement B : Every homomorphic image of a cyclic group is cyclic

The idempotent element in a group are

If number of left cosets of H in G are n and the number of right cosets of H in G are m, then

Given, permutation  is equivalent to

Every group of prime order is

Given, the permutation C = ( 1 2 3 4 5 6 7) then C³ is

If H₁ and H₂ are two right coset sets of Subgroup H₁, then