BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ángel del Río (Universidad de Murcia) DTSTART:20211021T160000Z DTEND:20211021T170000Z DTSTAMP:20260423T053141Z UID:GOThIC/41 DESCRIPTION:Title: A negative solution to the Modular Isomorphism Problem\nby Ángel del Río (Universidad de Murcia) as part of GOThIC - Ischia Online Group Theor y Conference\n\n\nAbstract\nLet $R$ be a ring. \nThe Isomorphism Problem f or group rings over $R$ asks whether the isomorphism type of a group $G$ i s determined by the isomorphism type of the group ring $RG$. \nThe special case where $R$ is a field with $p$ elements and $G$ is a finite $p$-group \, for $p$ prime\, is known as the Modular Isomorphism Problem. \n\nThe hi story of the Isomorphism Problem goes back to a seminal paper of G. Higman in the 1940s. The Modular Isomorphism Problem appeared in a survey paper by R. Brauer in 1963. While many relevant instances of the general Isomorp hism Problem have been already resolved\, the Modular Isomorphism Problem resisted until now. \n\nIn cooperation with Diego García and Leo Margolis we discovered recently two non-isomorphic groups of order $2^9$ whose gro up algebras over any field of characteristic $2$ are isomorphic. We will p resent this example and give an overview of the state of the art on the Is omorphism Problem.\n LOCATION:https://researchseminars.org/talk/GOThIC/41/ END:VEVENT END:VCALENDAR