Degree 1 and 2 representations of nilpotent groups and applications to units of group rings

DOI10.1007/BF02568007zbMath0834.16034MaRDI QIDQ1895722

Guilherme Leal, Eric Jespers

Publication date: 8 April 1996

Published in: Manuscripta Mathematica (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/156067

zbMATH Keywords

finite groupsgeneratorssubgroups of finite indexquaternion algebrasunit groupsdivision ringsintegral group ringsfinite nilpotent groupsrational group rings

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Group rings (16S34) Generators, relations, and presentations of groups (20F05) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Finite nilpotent groups, (p)-groups (20D15) Units, groups of units (associative rings and algebras) (16U60)

Related Items (12)

Unnamed Item ⋮ Groups of units of integral group rings commensurable with direct products of free-by-free groups. ⋮ Subgroup separability in integral group rings. ⋮ Rational group algebras of finite groups: from idempotents to units of integral group rings. ⋮ From the Poincaré Theorem to generators of the unit group of integral group rings of finite groups ⋮ Groups of units of integral group rings of Kleinian type ⋮ Finite generation of units in alternative loop rings ⋮ From Farey symbols to generators for subgroups of finite index in integral group rings of finite groups ⋮ A structure theorem for the unit group of the integral group ring of some finite groups ⋮ Central Idempotents and Units in Rational Group Algebras of Alternating Groups ⋮ UNITARY UNITS IN INTEGRAL GROUP RINGS ⋮ Congruence subgroups in group rings^*

Cites Work

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• Classification of finite subgroups of \(2\times 2\) matrices over a division algebra of characteristic zero
• Construction of units in group rings of monomial and symmetric groups
• Generators of large subgroups of the unit group of integral group rings
• Units of group rings of solvable and Frobenius groups over large rings of cyclotomic integers
• Generators of large subgroups of units of integral group rings of nilpotent groups
• Describing units of integral group rings of some 2-groups
• Construction of Units in Integral Group Rings of Finite Nilpotent Groups
• Units of group rings of groups of order 16
• Bicyclic and Bass Cyclic Units in Group Rings
• Units of Integral Group Rings of Some Metacyclic Groups
• Units of integral group rings of hamiltonian groups^*
• Bicyclic Units in some Integral Group Rings
• Finite Subgroups of Division Rings

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