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Suppose that H be an X-set and suppose that a∼b and |Xa|=|Xb|, the which of the following is true?

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Suppose that H be an X-set and suppose that a∼b and |Xa|=|Xb|, the which of the following is true?

(a) Xa is powerset of Xb

(b) Xa is isomorphic to Xb

(c) Xa is homomorphic to Xb

(d) Xb is the subset of Xa

This question was posed to me in an online interview.

My enquiry is from Groups topic in division Groups of Discrete Mathematics

1 Answer

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The correct answer is (b) Xa is isomorphic to Xb

For explanation I would say: According to Burnside theorem, Xa is isomorphic to Xb and in particular |Xa|=|Xb|.

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