1) An isomorphism form group G to G itself is called as a. monomorphism. b. automorphism. c. cpimorphism. d. cndomorphis

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1 An Isomorphism Form Group G To G Itself Is Called As A Monomorphism B Automorphism C Cpimorphism D Cndomorphis 1 (39.91 KiB) Viewed 31 times

1) An isomorphism form group G to G itself is called as a. monomorphism. b. automorphism. c. cpimorphism. d. cndomorphism. 2) A homomorphism which is one - to - one and onto is called as a. isomorphism. b. cpimorphism. c. cndomorphism. d. monomorphism. 3) Let ⟨S,+⟩ and ⟨S′,∗′⟩ are two binary structures. To determine two binary structures are isomorphic, the following steps must follow: i) Define the function of Φ that gives the isomorphism of S with S′. ii) Show that Φ is one-to-one function. iii) Show that Φ is onto S. iv) Show that Φ(a+b)=Φ(a)⋅∗′Φ(b) for all a,b in S. Which of the following steps are TRUE? a. i, ii and iii. b. i, iii and iv. c. ii, iii and iv. d. i, ii, iii and iv. 4) The inverse of an even permutation is a. odd permutation. b. even permutation. c. odd and even permutation. d. none of the above.
5) Suppose (2​4​6​) and ( 3​5​6​) are the two permutation groups that form cycles. The type of this permutation is a. acyclic. b. even. c. odd. d. prime. 6) Which theorem is suitable for the statement below: "Let H be a subgroup of a finite group G. Then, the order of H is a divisor of the order of Gnn a. Cayley's Theorem. b. Euler's Theorem. c. Lagrange's Theorem. d. None of the above. 7) Which theorem is suitable for the statement below: "A subgroup H of G is normal in G if and only if xHx−1⊆H for all x in G." a. Normal Subgroup Test. b. Euler's Theorem. c. Lagrange's Theorem. d. None of the above. 8) If H is a subgroup of G, then aH=Ha if and only if a. a∈H. b. b∈H. c. ab∈H. d. a−1b∈H. 9) Every group of order 5 is a. cyclic. b. cyclic but not Abelian. c. non-cyclic. d. non-cyclic but Abelian.