Free Groups and Subgroups of Finite Index in the Unit Group of an Integral Group Ring

DOI10.1080/00927870701404259zbMath1128.16017OpenAlexW1982353215MaRDI QIDQ5423811

Ann Dooms, Eric Jespers, Manuel Ruiz Marin

Publication date: 31 October 2007

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10317/1012

zbMATH Keywords

finite groupssubgroups of finite indexfree subgroupsinvolutionsgroups of unitsunit groupsintegral group ringsunitary unitscentral unitsfinite index subgroupsBass cyclic unitsbicyclic units

Mathematics Subject Classification ID

Subgroup theorems; subgroup growth (20E07) Group rings (16S34) Group rings of finite groups and their modules (group-theoretic aspects) (20C05) Rings with involution; Lie, Jordan and other nonassociative structures (16W10) Free nonabelian groups (20E05) Units, groups of units (associative rings and algebras) (16U60)

Related Items (9)

Bass units as free factors in integral group rings of simple groups. ⋮ Abelianization of the unit group of an integral group ring ⋮ BASS CYCLIC UNITS AS FACTORS IN A FREE GROUP IN INTEGRAL GROUP RING UNITS ⋮ 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 ⋮ Unitary Units Satisfying a Group Identity ⋮ Alternating units as free factors in the group of units of integral group rings ⋮ Involutions and free pairs of bicyclic units in integral group rings of non-nilpotent groups

Cites Work

• Unnamed Item
• Arithmetic subgroups of algebraic groups
• Isomorphic group (and loop) algebras
• Generators of large subgroups of the unit group of integral group rings
• Constructing free subgroups of integral group ring units
• Construction of Units in Integral Group Rings of Finite Nilpotent Groups
• UNITARY UNITS IN INTEGRAL GROUP RINGS
• Free Subgroups in the Unit Groups of Integral Group Rings
• On free subgroups of units of rings
• Groups of units of integral group rings of Kleinian type
• Groups generated by two bicyclic units in integral group rings
• Central units of integral group rings of nilpotent groups
• The Units of Group-Rings

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