A CHARACTERIZATION OF THE UNIT GROUP IN ℤ[T×C<sub>2</sub>]

Bilgin, Tevfik; Küsmüş, Ömer; Low, Richard M.

doi:10.4134/bkms.b150526

Bulletin of the Korean Mathematical Society

2016

DOI: 10.4134/bkms.b150526

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A CHARACTERIZATION OF THE UNIT GROUP IN ℤ[T×C₂]

Tevfik Bilgin¹,

Ömer Küsmüş²,

Richard M. Low³

Abstract: Abstract. Describing the group of units U (ZG) of the integral group ring ZG, for a finite group G, is a classical and open problem. In this note, we show that, where T = a, b : a 6 = 1, a 3 = b 2 , ba = a 5 b and F 97 , F 5 are free groups of ranks 97 and 5, respectively.

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2024

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On the Unit Group of the Integral Group Ring Z(S_3×C_3)

Küsmüş,

Denizler,

Low

2024

Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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Describing the group of units in the integral group ring is a famous and classical open problem. Let S_3 and C_3 be the symmetric group of order 6 and a cyclic group of order 3, respectively. In this paper, a description of the units of the integral group ring Z(S_3×C_3) of the direct product group S_3×C_3 concerning a complex representation of degree two is given. As a result, a part of the conjecture which is introduced in (Low, 2008) and related to group rings over a complex integral domain is resolved using representation theory.

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On the Unit Group of the Integral Group Ring Z(S_3×C_3)

Küsmüş,

Denizler,

Low

2024

Yüzüncü Yıl Üniversitesi Fen Bilimleri Enstitüsü Dergisi

View full text Add to dashboard Cite

show abstract

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A CHARACTERIZATION OF THE UNIT GROUP IN ℤ[T×C₂]

Abstract: Abstract. Describing the group of units U (ZG) of the integral group ring ZG, for a finite group G, is a classical and open problem. In this note, we show that, where T = a, b : a 6 = 1, a 3 = b 2 , ba = a 5 b and F 97 , F 5 are free groups of ranks 97 and 5, respectively.

Cited by 1 publication

References 17 publications

On the Unit Group of the Integral Group Ring Z(S_3×C_3)

On the Unit Group of the Integral Group Ring Z(S_3×C_3)

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A CHARACTERIZATION OF THE UNIT GROUP IN ℤ[T×C2]

Abstract: Abstract. Describing the group of units U (ZG) of the integral group ring ZG, for a finite group G, is a classical and open problem. In this note, we show that, where T = a, b : a 6 = 1, a 3 = b 2 , ba = a 5 b and F 97 , F 5 are free groups of ranks 97 and 5, respectively.

Cited by 1 publication

References 17 publications

On the Unit Group of the Integral Group Ring Z(S_3×C_3)

On the Unit Group of the Integral Group Ring Z(S_3×C_3)

Contact Info

Product

Resources

About

A CHARACTERIZATION OF THE UNIT GROUP IN ℤ[T×C₂]