The status of the Zassenhaus conjecture for small groups
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We identify all small groups of order up to 288 in the GAP Library for which the Zassenhaus conjecture on rational conjugacy of units of finite order in the integral group ring cannot be established by an existing method. The groups must first survive all theoretical sieves and all known restrictions on partial augmentations (the HeLP+ method). Then two new computational methods for verifying the Zassenhaus conjecture are applied to the unresolved cases, which we call the quotient method and the partially central unit construction method. To the cases that remain we attempt an assortment of special arguments available for units of certain orders and the lattice method. In the end, the Zassenhaus conjecture is verified for all groups of order less than 144 and we give a list of all remaining cases among groups of orders 144 to 287.
Bächle , A , Herman , A , Konovalov , A , Margolis , L & Singh , G 2018 , ' The status of the Zassenhaus conjecture for small groups ' , Experimental Mathematics , vol. 27 , no. 4 , pp. 431-436 . https://doi.org/10.1080/10586458.2017.1306814
© 2017, Taylor & Francis. This work has been made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at www.tandfonline.com / https://doi.org/10.1080/10586458.2017.1306814
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