Tag : group theory
- Which one of the following groups has elements of order 1,2,3,4,5 but does not have an element of order greater than or equal to 6 ?
- Consider the group G = {A ∈ M_2(R): AA^{T} = I_2} with respect to matrix multiplication. Let Z(G) = {A ∈ G : AB = BA, for all B ∈ G}. Then, the cardinality of Z(G) is
- Consider G = {m + n·sqrt2 : m,n ∈ Z} as a subgroup of the additive group ℝ. Which of the following statements is/are TRUE?
- Let G be a group of order 39 such that it has exactly one subgroup of order 3 and exactly one subgroup of order 13. Then, which one of the following statements is TRUE?
- Which one of the following is TRUE for the symmetric group S_{13}?
- For a positive integer n, let U(n) = {bar r ∈ Z_n : gcd(r, n) = 1} be the group under multiplication modulo n. Then, which one of the following statements is TRUE?
- Let G be a finite group containing a non-identity element which is conjugate to its inverse. Then, which one of the following is TRUE?