A note on magic rectangle set MRS Γ ( 2 k + 1 , 4 ; 4 l + 2 )

A Γ ‐magic rectangle set M R S Γ ( a , b ; c ) of order a b c is a set of c arrays of size ( a × b ) whose entries are elements of a finite Abelian group Γ of order a b c , each appearing once, with all row sums in each rectangle equal to a constant ω ∈ Γ and all column sums in each rectangle equal to a constant δ ∈ Γ . There is known a complete characteristic of a MRS Γ ( a , b ; c ) for { a , b } ≠ { 2 k + 1 , 2 α } for positive integers k , α . The case { a , b } = { 2 k + 1 , 2 α } is unsolved for α > 1 . In this paper we show that a MRS Γ ( 2 k + 1 , 4 ; 4 l + 2 ) exists if and only if the group Γ has more than one involution.