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Single elements.

Gardner, B.J., Mason, Gordon (2006)

Beiträge zur Algebra und Geometrie

Square subgroups of rank two abelian groups

A. M. Aghdam, A. Najafizadeh (2009)

Colloquium Mathematicae

Let G be an abelian group and ◻ G its square subgroup as defined in the introduction. We show that the square subgroup of a non-homogeneous and indecomposable torsion-free group G of rank two is a pure subgroup of G and that G/◻ G is a nil group.

Strongly 2-nil-clean rings with involutions

Huanyin Chen, Marjan Sheibani Abdolyousefi (2019)

Czechoslovak Mathematical Journal

A * -ring R is strongly 2-nil- * -clean if every element in R is the sum of two projections and a nilpotent that commute. Fundamental properties of such * -rings are obtained. We prove that a * -ring R is strongly 2-nil- * -clean if and only if for all a ∈ R , a 2 ∈ R is strongly nil- * -clean, if and only if for any a ∈ R there exists a * -tripotent e ∈ R such that a - e ∈ R is nilpotent and e a = a e , if and only if R is a strongly * -clean SN ring, if and only if R is abelian, J ( R ) is nil and R / J ( R ) is * -tripotent. Furthermore, we explore the structure...

Structure of the Unit Group of FD10

Khan, Manju (2009)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 16U60, 20C05.The structure of the unit group of the group algebra FD10 of the dihedral group D10 of order 10 over a finite field F has been obtained.Supported by National Board of Higher Mathematics, DAE, India.

Structure of the unit group of the group algebras of non-metabelian groups of order 128

Navamanirajan Abhilash, Elumalai Nandakumar, Rajendra K. Sharma, Gaurav Mittal (2025)

Mathematica Bohemica

We characterize the unit group for the group algebras of non-metabelian groups of order 128 over the finite fields whose characteristic does not divide the order of the group. Up to isomorphism, there are 2328 groups of order 128 and only 14 of them are non-metabelian. We determine the Wedderburn decomposition of the group algebras of these non-metabelian groups and subsequently characterize their unit groups.

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