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[PDF] Top 20 Describing units of integral group rings up to commensurability

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Describing units of integral group rings up to commensurability

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 ... See full document

21

Describing units of integral group rings up to commensurability

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] ... See full document

6

On the Gruenberg–Kegel graph of integral group rings of finite groups

On the Gruenberg–Kegel graph of integral group rings of finite groups

... trivial units of Z ...for integral group rings and if it is valid for a specific group G it provides of course a positive answer to the prime graph question for V ( Z ... See full document

12

LWE  from  Non-commutative  Group  Rings

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 ... See full document

22

The prime graph conjecture for integral group rings of some alternatings groups

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, 8, 9, 10, 12, 15 and ...investigate units of orders 2, 3, 5 and ...for units are: 14, 18, 20, 24, 30, 35, 45 and 63. We prove that ... See full document

11

Arithmetic rigidity and units in group rings

Arithmetic rigidity and units in group rings

... It is a consequence of the Borel Density Theorem [4] that a lattice in a connected linear semisimple Lie group admits, up to commensurability, an essentially unique decomposition into a product of ... See full document

13

Integral group rings with all central units trivial: Solvable groups

Integral group rings with all central units trivial: Solvable groups

... P ROOF : Let G be an odd-order group with the cut-property, so that G satisfies (1), i.e., in the terminology of Chillag-Dolfi [3], G is an inverse semi-rational group. Consequently, by ([3], Theorem 3) ... See full document

7

The Group of Units of Integral Group Rings of Extra-Special 2-Groups

The Group of Units of Integral Group Rings of Extra-Special 2-Groups

... on group rings is to describe precisely the group of units U (RG) of a group ring RG, where R is a commutative ring with identity and G is a finite ...the group of units ... See full document

12

Periodic rings with finitely generated underlying group

Periodic rings with finitely generated underlying group

... The structure theorem above shows that describing R effectively depends heavily on the structure of the finite ring T . In the case where T is a ring with identity, we can give a more precise description. Indeed, in ... See full document

6

Group Rings over the p-Adic Integers

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 ... See full document

130

The Tarski Theorems and Elementary Equivalence of Group Rings

The Tarski Theorems and Elementary Equivalence of Group Rings

... and rings and the corres- ponding universal and elementary theory of the formed group ...groups, rings and group ...the group G is elementarily equivalent to the group H and the ... See full document

15

On Azumaya Galois extensions and skew group rings

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, ... See full document

5

Multiple realization and the commensurability of taxonomies

Multiple realization and the commensurability of taxonomies

... neurophysiological practice of carving up the brain.” What they believe this examination reveals is, firstly, that the principle of psychological function plays an essential role in both disciplines, and secondly, ... See full document

24

COMMUTATIVE WEAKLY INVO–CLEAN GROUP RINGS

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 ... See full document

5

On an infinite integral linear group

On an infinite integral linear group

... has finite rank and k^X - k^ e f(i)A for all k^ e K^. Then the set of all such elements X is a normal subset of r and so generates a normal subgroup of T. T-Je could even use a descending chain vrhere each factor ... See full document

130

Language, culture and the quest for commensurability

Language, culture and the quest for commensurability

... The issue of incommensurability played a central role in the language and culture debates in English education by introducing the notion of relativism which acknow[r] ... See full document

239

On group rings and some of their applications to combinatorics and symmetric cryptography

On group rings and some of their applications to combinatorics and symmetric cryptography

... research, group rings also receive attention for their applica- tions to ...instance, group rings are directly used to construct key exchange protocols similar to the Diffe-Hellman protocol in ... See full document

14

On the Commensurability of Directional Distance Functions

On the Commensurability of Directional Distance Functions

... for units of measurement towards which others have to comply by commensurating their unit directional vectors with the same matrices that relate their units of measurement to that of this ... See full document

17

Serial group rings of finite groups. \(p\)-solvability

Serial group rings of finite groups. \(p\)-solvability

... Fact 4 ([9, Theorem 11]). Let F be an arbitrary field of characteristic p and let G be a finite p-nilpotent group with a cyclic p-Sylow subgroup. Then F G is a (left and right) principal ideal ring, in particular ... See full document

16

Commensurability effects in holographic homogeneous lattices.

Commensurability effects in holographic homogeneous lattices.

... The results which we get for the helical background are shown on figure 5. We span the same parameter space as in the previously considered case of Q-lattice. At large λ and large k the procedure calls for higher ... See full document

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