Normal Subgroups of the Free Group
نویسندگان
چکیده
We present a method of producing normal subgroups of the free group on r generators not containing a given word. Special attention is given to the normal subgroups of the free group on two generators. In considering the exponent sum of the generators in a given word, we produce such subgroups and clearly state for what class of words these subgroups are not easily obtainable. We also provide a general condition for skipping in p×q covers with a backbone, providing conditions in which skipping covers may be generalized to higher folds. Furthermore, we analyze certain infinite families of covers and show their relevance in enumerating covers of a given fold.
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