GROUPS THAT INVOLVE FINITELY MANY PRIMES AND HAVE ALL SUBGROUPS SUBNORMAL II

It is shown that if G is a hypercentral group with all subgroups subnormal, and if the torsion subgroup of G is a pi-group for some finite set pi of primes, then G is nilpotent. In the case where G is not hypercentral there is a section of G that is much like one of the well-known Heineken-Mohamed groups. It is also shown that if G is a residually nilpotent group with all subgroups subnormal whose torsion subgroup satisfies the above condition then G is nilpotent.

Semantic priming of familiar songs

We explored the functional organization of semantic memory for music by comparing priming across familiar songs both within modalities (Experiment 1, tune to tune; Experiment 3, category label to lyrics) and across modalities (Experiment 2, category label to tune; Experiment 4, tune to lyrics). Participants judged whether or not the target tune or lyrics were real (akin to lexical decision tasks). We found significant priming, analogous to linguistic associative-priming effects, in reaction times for related primes as compared to unrelated primes, but primarily for within-modality comparisons. Reaction times to tunes (e.g., "Silent Night") were faster following related tunes ("Deck the Hall") than following unrelated tunes ("God Bless America"). However, a category label (e.g., Christmas) did not prime tunes from within that category. Lyrics were primed by a related category label, but not by a related tune. These results support the conceptual organization of music in semantic memory, but with potentially weaker associations across modalities.

Lexical Development in Adult Beginning Second Language Learners

This research tests the hypothesis that knowledge of derivational morphology facilitates vocabulary acquisition in beginning adult second language learners. Participants were mono-lingual English-speaking college students aged 18 years and older enrolled inintroductory Spanish courses. Knowledge of Spanish derivational morphology was tested through the use of a forced-choice translation task. Spanish lexical knowledge was measured by a translation task using direct translation (English word) primes and conceptual (picture) primes. A 2x2x2 mixed factor ANOVA examined the relationships between morphological knowledge (strong, moderate), error type (form-based, conceptual), and prime type (direct translation, picture). The results are consistent with the existence of a relationship between knowledge of derivational morphology andacquisition of second language vocabulary. Participants made more conceptually-based errors than form-based errors F (1,22)=7.744, p=.011. This result is consistent with Clahsen & Felser’s (2006) and Ullman’s (2004) models of second language processing. Additionally, participants with Strong morphological knowledge made fewer errors onthe lexical knowledge task than participants with Moderate morphological knowledge t(23)=-2.656, p=.014. I suggest future directions to clarify the relationship between morphological knowledge and lexical development in adult second language learners.

Verifying Harder's Conjecture for Classical and Siegel Modular Forms

A conjecture by Harder shows a surprising congruence between the coefficients of “classical” modular forms and the Hecke eigenvalues of corresponding Siegel modular forms, contigent upon “large primes” dividing the critical values of the given classical modular form. Harder’s Conjecture has already been verified for one-dimensional spaces of classical and Siegel modular forms (along with some two-dimensional cases), and for primes p 37. We verify the conjecture for higher-dimensional spaces, and up to a comparable prime p.