Bicyclic units, Bass cyclic units and free groups

DOI10.1515/JGT.2008.014zbMath1144.16024arXivmath/0612091OpenAlexW2112494588MaRDI QIDQ5454349

Ángel Del Río, Jairo Z. Goncalves

Publication date: 28 March 2008

Published in: Journal of Group Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0612091

zbMATH Keywords

free subgroupsfree groupsBass cyclic unitsbicyclic unitsunits in integral group rings

Mathematics Subject Classification ID

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

Related Items (6)

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. ⋮ A SURVEY ON FREE SUBGROUPS IN THE GROUP OF UNITS OF GROUP RINGS ⋮ Involutions and free pairs of bicyclic units in integral group rings ⋮ From Farey symbols to generators for subgroups of finite index in integral group rings of finite groups ⋮ Alternating units as free factors in the group of units of integral group rings

Cites Work

• Generators of large subgroups of the unit group of integral group rings
• The Dirichlet unit theorem, induced characters, and Whitehead groups of finite groups
• Linear groups and group rings.
• FREE SUBGROUPS IN THE GROUP OF UNITS OF A TWISTED GROUP ALGEBRA
• Constructing free subgroups of integral group ring units
• Non-Free Points for Groups Generated by a Pair of 2×2 Matrices
• Construction of Units in Integral Group Rings of Finite Nilpotent Groups
• Free Subgroups in the Unit Groups of Integral Group Rings
• On free subgroups of units of rings
• Free Subgroups in the Units of ℤ[K₈ × C_p]
• Groups generated by two bicyclic units in integral group rings

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