For a, b, c, d ≥ 0 with ad − bc > 0, we consider the unilateral weighted shift S(a, b, c, d) with weights αn := √ an+b cn+d (n ≥ 0). Using Schur product techniques, we prove that S(a, b, c, d) is always subnormal; more generally, we establish that for every p ≥ 1, all p-subshifts of S(a, b, c, d) are subnormal. As a consequence, we show that all Bergman-like weighted shifts are subnormal.

An abundance of information regarding the structure of a finite group can be obtained by studying its irreducible characters. Of particular interest are monomial characters — those induced from a linear character of some subgroup — since Brauer has shown that any irreducible character of a group can be written as an integral linear combination of monomial characters. Our primary focus is the cl...

A subgroup H of a group G is called ss-quasinormal in G if there is a subgroup B of G such that G = HB and H permutes with every Sylow subgroup of B; H is called weakly s-permutable in G if there is a subnormal subgroup T of G such that G = HT and H ∩ T ≤ HsG, where HsG is the subgroup of H generated by all those subgroups of H which are s-permutable in G. We fix in every non-cyclic Sylow subgr...