On The Non-kth Elements of a Group
Abstract
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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