Johnson, F.E.A.;
(2001)
Arithmetic rigidity and units in group rings.
Transactions of the American Mathematical Society
, 353
(11)
pp. 4623-4635.
10.1090/S0002-9947-01-02816-1.
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Abstract
For any finite group G the group U(Z[G]) of units in the integral group ring Z[G]is an arithmetic group in a reductive algebraic group, namely the Zariski closure of SL1 (Q[G]). In particular, the isomorphism type of the Q-algebra Q[G] determines the commensurability class of U(Z[G]); we show that, to a large extent, the converse is true. In fact, subject to a certain restriction on the Q-representations of G the converse is exactly true.
| Type: | Article |
|---|---|
| Title: | Arithmetic rigidity and units in group rings |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1090/S0002-9947-01-02816-1 |
| Publisher version: | http://dx.doi.org/10.1090/S0002-9947-01-02816-1 |
| Language: | English |
| Additional information: | Published by the American Mathematical Society |
| UCL classification: | UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/9110 |
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