Let ℤn be the ring of integers modulo n. Let Ct , Em , and Fr,s respectively denote the cyclic group of order t, the elementary abelian 2-group of order 2m, and the abelian group of exponent 4 with order 2r4s. In this article, we find the structure and generators of the unit group V(ℤnC2). We also solve the normal complement problem in V(ℤnC2). Additionally, we provide a normal complement of Em in V(ℤ2nEm). At the end, we determine the structure of V(ℤpnFr,s) for an odd prime p and establish that Fr,s does not have a normal complement in V(ℤpnFr,s).
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Setia et al. (2024) studied this question.
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