University of Birmingham > Talks@bham > Algebra Seminar > Torsion Units in Integral Group Rings of Sporadic Simple Groups

## Torsion Units in Integral Group Rings of Sporadic Simple GroupsAdd to your list(s) Download to your calendar using vCal - Alexander Konovalov, University of St Andrews
- Thursday 11 March 2010, 16:00-17:00
- Watson Building, Lecture Room A.
If you have a question about this talk, please contact Simon Goodwin. (joint work with Victor Bovdi, Eric Jespers, Steve Linton, Salvatore Siciliano et al.) Let U( ZG) called the normalized unit group of ZG and denoted by V(ZG).The long-standing conjecture of H.Zassenhaus (ZC) says that every torsion unit from V( The criterion for ZC can be formulated in terms of vanishing of partial augmentations of torsion units (for an element of a group ring of the form Z and g in _{i}G, its partial augmentation with respect to the conjugacy class C of elements of the group G is the sum of coefficients a over those _{i}g which belong to the class _{i}C). Therefore, it is useful to know for each possible order of a torsion unit in V(ZG), which combinations of partial augmentations may arise.This motivated us to start the project to collect information about possible partial augmentations of torsion units of integral group rings of sporadic simple groups. As a consequence, at the time of this talk we proved that - Mathieu groups M
_{11}, M_{12}, M_{22}, M_{23}, M_{24}; - Janko groups J
_{1}, J_{2}, J_{3}; - Held, Higman-Sims, McLaughlin, Rudvalis and Suzuki groups.
In my talk I will summarise known information about orders and partial augmentations for these groups, explain enhancements of the Luthar-Passi method that were developed during the project, and highlight some challenges arising from the remaining sporadic simple groups. This talk is part of the Algebra Seminar series. ## This talk is included in these lists:Note that ex-directory lists are not shown. |
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