Abstract We obtain an effective analytic formula, with explicit constants, for the number of distinct irreducible factors a polynomial $f \in \mathbb {Z}[x]$ . use version Mertens’ theorem fields to estimate related sum over rational primes. For given , our result yields finite list primes that certifies f

the theorem 12 in [a note on $p$-nilpotence and solvability of finite groups, j. algebra 321(2009) 1555--1560.] investigated the non-abelian simple groups in which some maximal subgroups have primes indice. in this note we show that this result can be applied to prove that the finite groups in which every non-nilpotent maximal subgroup has prime index aresolvable.

What kinds of processing mechanisms determine the forms of spoken sentences? Three experiments (N 1⁄4 176) measured whether the mention of an optional that in a sentence-complement structure (‘‘The mechanic mentioned (that) the car could use a tune-up’’) can be primed by the prior production of a sentence that included a lexically or a lexically and syntactically similar that, using a recall-ba...

The present study used event-related potentials (ERPs) to investigate the function of signals induced by cognitive conflict during the detection stage and the resolution stage of perceptual processing. The study used a combination of the Stroop task and an affective priming task to examine the conflict priming effect when the stimulus onset asynchrony (SOA) was 200 ms or 800 ms. Behavioral resu...

Recent work suggests that people evaluate target stimuli within short and flexible time periods called evaluation windows. Stimuli that briefly precede a target (forward primes) or briefly succeed a target (backward primes) are often included in the target's evaluation. In this article, the authors propose that predictable forward primes act as "go" signals that prepare target processing, such ...