Unitary units of the group algebra of modular groups

Balogh, Zsolt

doi:10.1142/s021949882250027x

Cited by 3 publications

(1 citation statement)

References 13 publications

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“…The unitary subgroups have been proven to be very useful subgroups in several studies (see [2,3,4,6,7,10,11,13,14,15] and [16]). However, we know very little about their structure, as even finding their order is a challenging problem.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

The Order of the Unitary Subgroups of Group Algebras

Balogh¹

2022

Preprint

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Let F G be the group algebra of a finite p-group G over a finite field F of positive characteristic p. Let ⊛ be an involution of the algebra F G which is a linear extension of an anti-automorphism of the group G to F G. If p is an odd prime, then the order of the ⊛-unitary subgroup of F G is established. For the case p = 2 we generalize a result obtained for finite abelian 2-groups. It is proved that the order of the * -unitary subgroup of F G of a non-abelian 2-group is always divisible by a number which depends only on the size of F , the order of G and the number of elements of order two in G. Moreover, we show that the order of the * -unitary subgroup of F G determines the order of the finite p-group G.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

The Order of the Unitary Subgroups of Group Algebras

Balogh¹

2022

Preprint

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Modular group algebras whose group of unitary units is locally nilpotent

Bovdi¹

2022

Acta Sci. Math. (Szeged)

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The order of the unitary subgroups of group algebras

Balogh

2022

Int. J. Algebra Comput.

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Let [Formula: see text] be the group algebra of a finite [Formula: see text]-group [Formula: see text] over a finite field [Formula: see text] of positive characteristic [Formula: see text]. Let ⊛ be an involution of the algebra [Formula: see text] which is a linear extension of an anti-automorphism of the group [Formula: see text] to [Formula: see text]. If [Formula: see text] is an odd prime, then the order of the ⊛-unitary subgroup of [Formula: see text] is established. For the case [Formula: see text] we generalize a result obtained for finite abelian [Formula: see text]-groups. It is proved that the order of the ∗-unitary subgroup of [Formula: see text] of a non-abelian [Formula: see text]-group is always divisible by a number which depends only on the size of [Formula: see text], the order of [Formula: see text] and the number of elements of order two in [Formula: see text]. Moreover, we show that the order of the ∗-unitary subgroup of [Formula: see text] determines the order of the finite [Formula: see text]-group [Formula: see text].

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Unitary units of the group algebra of modular groups

Cited by 3 publications

References 13 publications

The Order of the Unitary Subgroups of Group Algebras

The Order of the Unitary Subgroups of Group Algebras

Modular group algebras whose group of unitary units is locally nilpotent

The order of the unitary subgroups of group algebras

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