 Affine semidirect product of cyclic groups of orders eleven and five

ID: affine-semidirect-product-of-cyclic-groups-of-orders-eleven-and-five

Codex  0 Created 2026-09-24 Updated 2026-10-03

Let

Q

be the subgroup of nonzero squares in

F_{11}^{\times}

. The affine maps

x ⟼ r x + b, r \in Q, b \in F_{11},

form the nonabelian semidirect product

C_{11} ⋊ C_{5}

(r, b) (s, c) = (rs, b + rc) .

 New to topics? Read the docs here!