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

Kumar, Yogesh; Sharma, R. KI.; Srivastava, J. B.

Acta Math. Acad. Paedagog. Nyházi. (N.S.) 33, 187-193 (2018).

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

Keywords:

group algebra; Wedderburn decomposition; unit group 187