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Element structure of general semilinear group of degree two over a finite field

This article gives specific information, namely, element structure, about a family of groups, namely: general semilinear group of degree two.
View element structure of group families | View other specific information about general semilinear group of degree two

This article describes the element structure of the general semilinear group of degree two over a finite field of size q = p^r, where p is the characteristic of the field. The Galois group of the extension \mathbb{F}_q/\mathbb{F}_p is a cyclic group of order r, generated by the p-power map (the Frobenius automorphism). Note that r = \log_p q

Contents

Summary

Item Value
order of the group r(q^2 - 1)(q^2 - q)
number of conjugacy classes PLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE]