On The Non-kth Elements of a Group
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In Abstract Algebra, raising an element to a certain power can provide insight on various properties of both the element itself and the group it is a part of. This thesis is interested in the number of elements of a group that cannot be represented as a fixed power of any element in the group. Interesting patterns emerge when we compare such values for non-isomorphic groups of the same order. Specifically, we compare the group of Integers Modulo 2n and the corresponding Dihedral group with the same order. We then expand to more general cases of direct and semidirect products.
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