Joe Kirtland
Levi Properties and Levi Formations
In group theory, abelian groups are a special class of groups. While it is far from true in the infinite case, abelian groups have been completely classified in the finite case. What many people have done to move beyond this is to study groups that are "almost" abelian. One avenue was taken by F.W. Levi in a 1942 paper where he studied groups G where [[a,b],c] = [a,[b,c]] for all elements a,b, and c in G. He called these groups L-groups. Levi was able to prove that a group G is an L-group if and only if <a>^G (the normal closure of a in G) is abelian for all elements a in G. This has lead to the following concept: A group G has L(E), the Levi property generated by E (a group theoretic property), if and only if <a>^G has property E for all elements a in G. The goal is then to study groups in which the normal closure of each element has a certain group theoretic property. It can also be shown that if the property E generates a subgroup closed formation, then L(E) is also a subgroup closed formation.
This talk is aimed at the strong undergraduate to graduate student and professional level. All are welcome, but audience members must come appropriately attired.
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