Word Count : 202

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Let (G = \langle g \rangle) be a cyclic group and let (H) be a non-trivial subgroup of (G). Since (G) is cyclic, every element of (G) can be written as (g^n) for some integer (n). Let (h \in H) be a non-identity element. Then (h = g^m) for some _____ _______ ________ ________ ______ _______ __________ ___.
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____ ___ ____ _____ _______ __________.
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________ __________ ________ ______ ___ ____ _________ _____ _______.
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________ __________ ___ __________ _____ ___.
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________ ______ __________ ___ _____ _________ _______ _________ _____ ____ ___.
___ ________ ________ __________ ______ _____ _____ _______.
______ ___ _______ __________ ___.
_______ ____ ___ __________ ______ __________ _____ ____.
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____ ___ ______ ________ ____.
___ ______ _______ ________.
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