Central units of integral group rings of nilpotent groups

DOI10.1090/S0002-9939-96-03398-9zbMath0846.16028OpenAlexW1537177585WikidataQ116166871 ScholiaQ116166871MaRDI QIDQ4875552

Eric Jespers, Sudarshan K. Sehgal, Michael M. Parmenter

Publication date: 25 September 1996

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-96-03398-9

zbMATH Keywords

subgroups of finite indexfinitely generated nilpotent groupsunit groupsintegral group ringscentral unitscentral Bass units

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Group rings (16S34) Group rings of infinite groups and their modules (group-theoretic aspects) (20C07) Nilpotent groups (20F18) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Units, groups of units (associative rings and algebras) (16U60)

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On idempotents and the number of simple components of semisimple group algebras, Unnamed Item, Central units of integral group rings of monomial groups, Integral group rings with all central units trivial, Bass units as free factors in integral group rings of simple groups., Rational group algebras of finite groups: from idempotents to units of integral group rings., Central units of the integral group ring $\mathbb {Z}A_5$, Isomorphisms of integral group rings of infinite groups, Central Units in Metacyclic Integral Group Rings, Construction of central units in integral group rings of finite groups, Central units of integral group rings, Free Groups and Subgroups of Finite Index in the Unit Group of an Integral Group Ring, From the Poincaré Theorem to generators of the unit group of integral group rings of finite groups, Central units of integral group rings^*, INTEGRAL GROUP RINGS WITH TRIVIAL CENTRAL UNITS II, On hypercentral units in integral group rings, On the normalizer problem., From Farey symbols to generators for subgroups of finite index in integral group rings of finite groups, Units of ℤ(C_p × C₂) and ℤ(C_p × C₂ × C₂), Central Idempotents and Units in Rational Group Algebras of Alternating Groups, UNITARY UNITS IN INTEGRAL GROUP RINGS, Central Units in ℤC_p,q, Congruence subgroups in group rings^*, On the index of a free abelian subgroup in the group of central units of an integral group ring.

Cites Work

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• Units of group rings of solvable and Frobenius groups over large rings of cyclotomic integers
• The Dirichlet unit theorem, induced characters, and Whitehead groups of finite groups
• Construction of Units in Integral Group Rings of Finite Nilpotent Groups
• Integral Group Rings with Trivial Central Units