Unit groups of group algebras of groups of order 18

Let [Formula: see text] be a group, [Formula: see text] be a finite field with a positive characteristic [Formula: see text], then [Formula: see text] is the group algebra of a group [Formula: see text] over [Formula: see text] with a positive characteristic [Formula: see text]. In this paper, the normal complement problem on semisimple group algebra [Formula: see text] is examined. The normal complement problem of groups of order up to 16 in their corresponding unit groups [Formula: see text] has already been discussed. We have proved that up to isomorphism all the three non-abelian groups of order 18 and up to isomorphism all three non-abelian groups of order 20 do not have normal complement in their corresponding unit groups [Formula: see text].

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Unit group of some finite semisimple group algebras

Arvind

Panja

2022

J Egypt Math Soc

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We provide the structure of the unit group of $${\mathbb {F}}_{p^k}S_n$$ F p k S n , where $$p>n$$ p > n is a prime and $$S_n$$ S n denotes the symmetric group on n letters. We also provide the complete characterization of the unit group of the group algebra $${\mathbb {F}}_{p^k}A_6$$ F p k A 6 for $$p\ge 7$$ p ≥ 7 , where $$A_6$$ A 6 is the alternating group on 6 letters.

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Unit groups of group algebras of groups of order 18

Cited by 5 publications

References 8 publications

Group of Units of Finite Group Algebras for Groups of Order 24

Group of Units of Finite Group Algebras for Groups of Order 24

On the normal complement problem of finite group algebra

Unit group of some finite semisimple group algebras

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