Question

Let G be finite set, which is a group under some operation and H be a subgroup and $a \in H$. Considering their order cardinality in increasing order :
A. $O(G)$

B. $O(a)$

C. $O(H)$

D. $Card(2^G)$

Choose the correct answer from the options given below :

• A. B, C, A, D
• B. D, B, C, A
• C. D, B, A, C
• D. B, C, D, A

Hint:

In group theory hierarchy: Element $\leq$ Subgroup $\leq$ Group. Power sets always result in the largest cardinality due to exponential growth.

Answer 1

The Correct Option is A