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Hayat, Umar; López-Aguayo, Daniel; Abbas, Akhtar
Symmetry (Basel), 07/2018, Volume: 10, Issue: 7Journal Article
Let G=Zp⊕Zp2, where p is a prime number. Suppose that d is a divisor of the order of G. In this paper, we find the number of automorphisms of G fixing d elements of G and denote it by θ(G,d). As a consequence, we prove a conjecture of Checco-Darling-Longfield-Wisdom. We also find the exact number of fixed-point-free automorphisms of the group Zpa⊕Zpb, where a and b are positive integers with a<b. Finally, we compute θ(D2q,d), where D2q is the dihedral group of order 2q, q is an odd prime, and d∈{1,q,2q}.
