Note on Paragraph 2, P. 533

A Note on P-sets

A P-set is a set S of positive integers such that no element of S divides the sum of any two (not necessarily being different) larger elements. Erdös and Sárközy [2] conjectured that there exists a constant c > 0 such that for every P-set S we have |{s ∈ S : s ≤ N}| < N1−c for infinitely many integers N . For P-sets S consisting of pairwise coprime integers this conjecture has been proved by T....

A note on p-curvatures

In this note, we give an arithmetic criterion for the Lie-irreducibility of linear differential equations based on p-curvatures.

a note on the normalizer of sylow 2-subgroup of special linear group $sl_2(p^f)$

let $g={rm sl}_2(p^f)$ be a special linear group and $p$ be a sylow‎ ‎$2$-subgroup of $g$‎, ‎where $p$ is a prime and $f$ is a positive‎ ‎integer such that $p^f>3$‎. ‎by $n_g(p)$ we denote the normalizer of‎ ‎$p$ in $g$‎. ‎in this paper‎, ‎we show that $n_g(p)$ is nilpotent (or‎ ‎$2$-nilpotent‎, ‎or supersolvable) if and only if $p^{2f}equiv‎ ‎1,({rm mod},16)$‎.

A note on cyclic codes over GR(p 2, m) of length p k

The number of self-dual cyclic codes of length pk over GR(p2,m) is determined by the nullity of a certain matrix M(pk, i1). With the aid of Genocchi numbers, we determine the nullity of M(pk, i1) and hence determine completely the number of such codes.

A Note on Weighted Composition Operators on L^p-Spaces