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The structure of the unit group of the group algebra \(\mathbb F S_5\) where \(\mathbb F\) is a finite field with char(\(\mathbb F\)) \(= p > 5\). (English) Zbl 1413.16053
Summary: Let \(\mathbb F_q\) denote a field having \(q = p^n\) elements, where \(p\) a prime, and let \(S_5\) denote the symmetric group of degree 5. We give a complete structure of the unit group \(\mathcal U(\mathbb F_qS_5)\), \(p > 5\).
MSC:
16U60 Units, groups of units (associative rings and algebras)
20C05 Group rings of finite groups and their modules (group-theoretic aspects)
16S34 Group rings
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