caa a22 4500 606244727 CHVBK 20210128101331.0 cr unu---uuuuu 210128e20150501xx s 000 0 eng 10.1007/s12044-015-0228-5 doi (NATIONALLICENCE)springer-10.1007/s12044-015-0228-5 Revisiting the Zassenhaus conjecture on torsion units for the integral group rings of small groups [Elektronische Daten] [ALLEN HERMAN, GURMAIL SINGH] In recent years several new restrictions on integral partial augmentations for torsion units of ℤG $\mathbb {Z} G$ have been introduced, which have improved the effectiveness of the Luthar-Passi method for checking the Zassenhaus conjecture for specific groups G. In this note, we report that the Luthar-Passi method with the new restrictions are sufficient to verify the Zassenhaus conjecture with a computer for all groups of order less than 96, except for one group of order 48 - the non-split covering group of S 4, and one of order 72 of isomorphism type (C 3 × C 3) ⋊ D 8. To verify the Zassenhaus conjecture for this group we give a new construction of normalized torsion units of ℚG $\mathbb {Q} G$ that are not conjugate to elements of ℤG $\mathbb {Z} G$ . Indian Academy of Sciences, 2015 Integral group rings nationallicence torsion units nationallicence Zassenhaus conjectures nationallicence HERMAN ALLEN Department of Mathematics and Statistics, University of Regina, S4S 0A2, Regina, Canada aut SINGH GURMAIL Department of Mathematics and Statistics, University of Regina, S4S 0A2, Regina, Canada aut Proceedings - Mathematical Sciences Springer India 125/2(2015-05-01), 167-172 0253-4142 125:2<167 2015 125 12044 https://doi.org/10.1007/s12044-015-0228-5 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s12044-015-0228-5 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- HERMAN ALLEN Department of Mathematics and Statistics, University of Regina, S4S 0A2, Regina, Canada aut NATIONALLICENCE 700 1- SINGH GURMAIL Department of Mathematics and Statistics, University of Regina, S4S 0A2, Regina, Canada aut NATIONALLICENCE 773 0- Proceedings - Mathematical Sciences Springer India 125/2(2015-05-01), 167-172 0253-4142 125:2<167 2015 125 12044