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Generating Sequences of Finite Groups
If you have a question about this talk, please contact Joanna Fawcett.
In an analogy with bases in vector spaces, one can define a notion of independent generating sets for a group. While these sets share some properties with vector space bases, in general they are very different. In particular, one important fact about n-dimensional vector space bases is that given a set of m < n linearly independent vectors, one can replace m of the original basis vectors with the new set. This property has been studied in the context of groups under the name of the replacement property. We will discuss the replacement property for groups and how it can be used to study the independent generating sequences of finite groups. Then, we will focus on a particular example in the family of groups PSL . The collaboration for this research includes Keith Dennis (Cornell) and Dan Collins (Princeton).
This talk is part of the Junior Algebra/Logic/Number Theory seminar series.
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