A A note on the Jacobson radical J ( 𝔽 2 n D 2 m )

UDC 512.5 The dimension of the Jacobson radical J ( 𝔽 2 n D 2 m ) and the algebraic structure of 𝔽 2 n D 2 k 3 J ( 𝔽 2 n D 2 k 3 ) are determined. Here, D 2 m represents the dihedral group of order 2 m , 𝔽 2 n represents any finite field of characteristic 2 , and F 2 n D 2 m represents the group algebra of the group D 2 m over the field 𝔽 2 n .