BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Charles Cox (University of Bristol) DTSTART:20210125T090000Z DTEND:20210125T100000Z DTSTAMP:20260423T052929Z UID:SiN/13 DESCRIPTION:Title: Spr ead and infinite groups\nby Charles Cox (University of Bristol) as par t of Symmetry in Newcastle\n\n\nAbstract\nMy recent work has involved taki ng questions asked for finite groups and considering them for infinite gro ups. There are various natural directions with this. In finite group theor y\, there exist many beautiful results regarding generation properties. On e such notion is that of spread\, and Scott Harper and Casey Donoven have raised several intriguing questions for spread for infinite groups (in htt ps://arxiv.org/abs/1907.05498). A group $G$ has spread $k$ if for every $g _1\, \\dots\, g_k \\in G$ we can find an $h \\in G$ such that $\\langle g_ i\, h \\rangle = G$. For any group we can say that if it has a proper quot ient that is non-cyclic\, then it has spread 0. In the finite world there is then the astounding result - which is the work of many authors - that t his condition on proper quotients is not just a necessary condition for po sitive spread\, but is also a sufficient one. Harper-Donoven’s first que stion is therefore: is this the case for infinite groups? Well\, no. But t hat’s for the trivial reason that we have infinite simple groups that ar e not 2-generated (and they point out that 3-generated examples are also k nown). But if we restrict ourselves to 2-generated groups\, what happens? In this talk we’ll see the answer to this question. The arguments will b e concrete (*) and accessible to a general audience.\n\n(*) at the risk of ruining the punchline\, we will find a 2-generated group that has every p roper quotient cyclic but that has spread zero.\n LOCATION:https://researchseminars.org/talk/SiN/13/ END:VEVENT END:VCALENDAR