Abstract
We develop a criterion for rational conjugacy of torsion units of the integral group ringℤG of a finite groupG, as also a necessary condition for an element ofℤG to be a torsion unit, and apply them to verify the Zassenhaus conjecture in case whenG=A 5.
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References
Berman S D, On the equationX m=1 in an integral group ring,Ukr. Math. Z. 7 (1955) 253–261
Burnside W,Theory of groups of finite order (Cambridge: Dover Publications) (1955)
Marciniak Z, Ritter J, Sehgal S K and Weiss A, Torsion units in integral group rings of some metabelian groups, II.J. Number Theory 25 (1987) 340–352
Polcino C Milies and Sehgal S K, Torsion units in integral group rings of metacyclic groups,J. Number Theory 19 (1984) 103–114
Sehgal S K,Topics in group rings (New York: Dekker) (1978)
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Luthar, I.S., Passi, I.B.S. Zassenhaus conjecture forA 5 . Proc. Indian Acad. Sci. (Math. Sci.) 99, 1–5 (1989). https://doi.org/10.1007/BF02874643
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DOI: https://doi.org/10.1007/BF02874643