Let G be a finite group with a nilpotent maximal subgroup S and let P denote the 2-Sylow subgroup of S. It is shown that if P ∩ Q is a normal subgroup of P for any 2-Sylow subgroup Q of G, then G is solvable.

The authors prove two theorems. The first theorem generalizes theorems due to T. Singh and O.P. Varshney, concerning absolute Nörlund summability of Fourier series of functions of bounded variation. The second theorem generalizes theorems of L.S. Bosanquet and H.P. Dikshit.

Let {Xn} be a sequence of independent identically distributed random variables and let The rate of convergence of probabilities , where 2 > r > 1, is studied.

Relationships between the numbers of general graphs and the numbers of multigraphs are set up with a view to enumerating multigraphs with a given partition. In the process of doing so certain structures which we call graph-lattices evolve. The principle of inclusion-exclusion plays an important part in the formulation of theorems and actual numerical results are computed with the aid of S-functions.

The results in the first parts of Theorems 2 and 3 of the paper in the title (see [2]) have been previously obtained by B.M. Schein in Theorem 1.12, page 299 [4], and in Proposition 1.13 (combined with the last paragraph of page 300) [4], respectively. To deduce the first part of Theorem 2 [2] from Theorem 1.12 [4] one merely uses the fact that a binary relation R on a set X satisfies RR−1R ⊆ R if if and only if it satisfies: R{x) ∩ R(y) ≠ □ implies R(x) = R(y), for any x, y ∈ X (see Proposition 9, page 132 [3]).

The Editor regrets that two errors have appeared in [1], through no fault of the author's. On page 325 the result (3.5) and the two lines following it should read:

where

On page 328 the result (4.3) and the two lines following it should read:

where