Dolph Algebras and Dolph Groups
DOI:
https://doi.org/10.17268/sel.mat.2023.02.11Keywords:
Finite groups, crossed products, 2-cocycle, group of units, Dolph algebrasAbstract
A finite Hopf crossed product whose base ring is a finite field will be called a Dolph algebra, and the corresponding group of units will be called a Dolph group. Assuming known the crossed product of a ring and a group under a crossed mapping [1], the units of the cross products Z2[X] ⟨X2⟩ ⋊f C2 and Z3[X] ⟨X2⟩ ⋊f C2 are calculated. Furthermore, we give concrete examples of 4 classes of Hopf crossed products.
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