Units in integral group rings
Describing units of integral group rings up to commensurability
... a group G we denote by U (ZG) the unit group of the integral group ring ...cyclic group, then the so-called Bass cyclic units generate a subgroup of finite index in U ...unit ...
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Units in $\mathbb{Z}_2(C_2\times D_\infty)$
... Sehgal, Units in Integral Group Rings , Longman Scientific and Technical, Harlow, 1993... Sharma[r] ...
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On the Gruenberg–Kegel graph of integral group rings of finite groups
... Remarks. Instead of [34, Theorem 2.7] we could have used the stronger result [23, Theorem 2.3] which says that partial augmentations of a torsion unit of Z G are non-zero only for conjugacy classes of G whose ...
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Integral group rings with all central units trivial: Solvable groups
... Converse follows easily from (1) by observing that 5 is a primitive root of 7 and of 3 b , for all b ≥ 1, 3 is a primitive root of 5, and the fact that U (Z/2 n Z) = h±1i ⊕ h3i, n ≥ 3. 2 Recall that an element x ∈ G is ...
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The Group of Units of Integral Group Rings of Extra-Special 2-Groups
... Bass units and bicyclic ...Bass units together with the bicyclic units generate a subgroup of nite index, the groups excluded are determined by the existence of exceptional simple components of Q G ...
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Describing units of integral group rings up to commensurability
... Permanent repository link: http://openaccess.city.ac.uk/13180/ Link to published version: http://dx.doi.org/10.1016/j.jpaa.2014.09.031 Copyright and reuse: City Research Online aims to m[r] ...
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The prime graph conjecture for integral group rings of some alternatings groups
... The group G possesses elements of orders 2, 3, 4, 5, 6, 7, 9, 10, 12 and ...investigate units of orders 2, 3, 5, 7 and ...for units are: 14, 18, 20, 24, 30, 35, 45 and 63. We prove that units ...
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Torsion units for some projected special linear groups
... torsion units of integral group rings of groups of small order (Groups, rings and group rings, Chapman & Hall/CRC, Boca Raton, FL), ...GAP Group, GAP- Groups, ...
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The status of the Zassenhaus conjecture for small groups
... The Zassenhaus conjecture for torsion units of integral group rings states that any torsion unit of Z G should be conjugate in Q G to a unit of ±G [21]. By [19, (37.5)] it suffices to ...
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LWE from Non-commutative Group Rings
... the group of integral units in a number field is a direct product of a finite group with a free abelian group, whose generators are known as fundamental ...the units are sent to ...
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Group Rings over the p-Adic Integers
... In this section we let A be a finite-dimensional semisimple K-algebra, and assume that K is complete. We give a summary of the theory of graduated orders in such algebras, which is a well-understood class of orders ...
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A sterically constrained bis(2,2′:6′,2′′ terpyridine) ligand
... hydrate [1.491 (3) AÊ; Chen et al., 1996]. The spanning poly- ether chain is suf®ciently long and ¯exible to allow the biphenyl unit to adopt a twisted con®guration with almost perpendicular rings. The torsion ...
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Periodic rings with finitely generated underlying group
... periodic rings with finitely generated un- derlying abelian group reduces to knowing the finite rings, the periodic rings which are free of finite rank as groups, and computing some ring ...
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On Azumaya Galois extensions and skew group rings
... [1] R. Alfaro and G. Szeto, The centralizer on H-separable skew group rings, Rings, extensions, and cohomology (New York), Lecture Notes in Pure and Appl. Math., vol. 159, Marcel Dekker, Inc., 1994, ...
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COMMUTATIVE WEAKLY INVO–CLEAN GROUP RINGS
... A criterion for an arbitrary commutative group ring to be nil-clean was recently obtained in [8]. Specifically, the following holds: A commutative ring R[G] is nil-clean if, and only if, the ring R is nil-clean ...
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The Tarski Theorems and Elementary Equivalence of Group Rings
... In the finitely generated case, the answer is yes, and both the Kharlampovich- Myasnikov solution and the Sela solution provide a complete characterization of the finitely generated elementary free groups. In the ...
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Serial group rings of finite groups. \(p\)-solvability
... Let F be a field of characteristic p and G is a finite group of order divisible by p. The group ring R = F G is artinian, therefore the seriality criterion (Fact 2) is applicable to R. Furthermore because R ...
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On partial Galois Azumaya extensions
... skew group ring to be ...for group rings, Szeto and Wong [19] for twisted group rings, and Ikehata [12] for skew group ring over commutative ...
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On some aspects of the theory of modules over group rings
... the action of 𝐻 on 𝐴 can be uniquely extended to the action of 𝐻 on 𝐸. In this case, we come to a module 𝐹 𝐺 where 𝐹 is a field. This shows that the case when a scalar ring of the group ring is a field is a major ...
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A CCA secure cryptosystem using matrices over group rings
... a group ring of a (rather small) symmetric group as the plat- form and discuss security of this scheme by addressing the Decision Diffie-Hellman (DDH) and Computational Diffie-Hellman (CDH) problems for that ...
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