Host Institution: 
La Trobe University 
Title of Seminar: 
Classifying finite pgroups by coclass 
Speaker's Name: 
Dr Heiko Dietrich 
Speaker's Institution: 
Monash University 
Time and Date: 
Friday 8 November, 2.00pm (AEDT) 
Seminar Abstract: 
One of the major themes in group theory is the classification of groups up to isomorphism. A famous example is the 'Classification Theorem of Finite Simple Groups', which classifies all finite simple groups  the basic building blocks of all finite groups. However, even if we restrict attention to the least complicated finite simple group, the cyclic group of prime order p, it is still an intricate problem to put these groups together in order to construct all groups of ppower order, socalled finite pgroups, up to isomorphism. One approach for classifying finite pgroups is to fix the order, say p^n, and to classify all groups having this order. However, already for small n this problem becomes intractable. In this talk, we discuss an alternative approach, namely, a classification of pgroups by "coclass". If the coclass is fixed, say r, then the finite pgroups of coclass r (up to isomorphism) define an infinite graph, the socalled coclass graph G(p,r). This graph has some remarkable periodic structures, which are reflected in the structures of the groups. We will discuss the structure of this graph, some classification results, and some open conjectures. 


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