# The Status of the Zassenhaus Conjecture for Small Groups

@article{Bchle2018TheSO, title={The Status of the Zassenhaus Conjecture for Small Groups}, author={Andreas B{\"a}chle and Allen Herman and Alexander Konovalov and Leo Margolis and Gurmail Singh}, journal={Experimental Mathematics}, year={2018}, volume={27}, pages={431 - 436} }

ABSTRACT 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… Expand

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