Thursday 26 September 2024 at 2:30 pm, as part of the Al@Bicocca seminar cycle, Jessica Anzanello (University of Padova) will talk about
Title: The Chebotarev invariant of a direct product of non-abelian finite simple groups
Abstract: A subset {g1, . . . , gt} of a finite group G invariably generates G if {g x1 1 , . . . , gxt t } generates G for every t-tuple (x1, . . . , xt) ∈ Gt . In this talk, I will answer the following questions. Let G be a direct product of k non-abelian finite simple groups. If we choose random elements from G independently, with replacement, and with the uniform distribution, how many should we expect to pick until the elements chosen generate G? And how many to invariably generate G? To do this, I will introduce an invariant that is related to problems in Galois theory, called the Chebotarev invariant C(G) of G, which is the expected value of the random variable n that is minimal subject to the requirement that n randomly chosen elements of G invariably generate G.
This is joint work with A. Lucchini and G. Tracey.
Information to attend in presence:
The seminar will be held in Room 3014 (3rd Floor) - U5 Building, University of Milano-Bicocca
Information to attend online:
Visit the page https://unimib.webex.com/unimib/j.php?MTID=m326713f82e2670958c5336df29992a6d