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Zassenhaus conjecture for \(S_ 5\). (English) Zbl 0729.16021

This is a continuation of an article by I. B. S. Passi and the first author [cf. Proc. Indian Acad. Sci., Math. Sci. 99, 1-5 (1989; Zbl 0678.16008)]. Performing very carefully more or less direct computations, the authors succeed in showing that every unit of \(ZS_ 5\) of one of the orders 2, 4, 6 is conjugate, under a unit of \(QS_ 5\), to an element of the symmetric group \(S_ 5\) itself.

MSC:

16U60 Units, groups of units (associative rings and algebras)
16S34 Group rings
20C05 Group rings of finite groups and their modules (group-theoretic aspects)

Citations:

Zbl 0678.16008
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References:

[1] James G., Encyclopedia of Mathematics and it’s applications 16 (1981)
[2] Ledermann Walter, Introduction to group characters (1977)
[3] DOI: 10.1007/BF02874643 · Zbl 0678.16008
[4] Marciniak Z., J.No.Th.25 99 pp 340– (1987)
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