बाह्य प्रत्यक्ष गुणन समूह ℤ30 ⊕ ℤ12 में अवयव (5, 3) की कोटि (order) __________ है।

Let G be a finite group of order n. Cayley's theorem states that G is isomorphic to a subgroup of the symmetric group Sk. What is the smallest general value of k that guarantees this embedding for any group of order n?

Let R = {0, 2, 4} be a subset of ℤ6. Which of the following options is true with respect to the operations of addition modulo 6 and multiplication modulo 6?