## 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)

### Keywords:

Zassenhaus conjecture; unit; symmetric group

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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