Friday, May 12, 2006; Noon-1pm Sc N321

Speaker: Dr. Bill Nico, Professor, Math/CS CSUEB

Partly motivated by the prime factorization of integers one can look at the correspondence between functions and equivalence relations in sets, homomorphisms and congruences in monoids, homomorphisms and subgroups in groups. The Jordan-Holder Theorem characterizes the decomposition. The group extension problem concerns re-assembling parts. The Schreier approach is well known, but the Krasner-Kaloujnine approach using the "produit complet" (aka "wreath product") of transformations is less well known. The former leads to group cohomology, while the latter may generalize to monoids and categories.