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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
##### Keywords:
group algebra; Wedderburn decomposition; unit group 187