scholarly journals On the structure of a group whose orbits on a finite module are the orbits of a proper subgroup

1985 ◽  
Vol 94 (2) ◽  
pp. 364-381 ◽  
Author(s):  
Trevor Hawkes ◽  
Graham Jones
Keyword(s):  
Proper Subgroup ◽  
Finite Module

scholarly journals Markov chains with exponential return times are finitary

2020 ◽  
pp. 1-9
Author(s):  
OMER ANGEL ◽  
YINON SPINKA
Keyword(s):  
Markov Chain ◽  
Markov Chains ◽  
Renewal Process ◽  
Proper Subgroup ◽  
Ergodic Markov Chain ◽  
Countable State Space ◽  
Return Times ◽  
Exponential Tails ◽  
Stationary Version ◽  
Countable State

Abstract Consider an ergodic Markov chain on a countable state space for which the return times have exponential tails. We show that the stationary version of any such chain is a finitary factor of an independent and identically distributed (i.i.d.) process. A key step is to show that any stationary renewal process whose jump distribution has exponential tails and is not supported on a proper subgroup of ℤ is a finitary factor of an i.i.d. process.

Rational permutation groups containing a full cycle

2013 ◽  
Vol 63 (6) ◽  
Author(s):  
Temha Erkoç ◽  
Utku Yilmaztürk
Keyword(s):  
Symmetric Group ◽  
Proper Subgroup ◽  
Symmetric Groups ◽  
Transitive Permutation Group ◽  
Rational Group ◽  
Prime Degree ◽  
A Finite Group ◽  
Rational Groups ◽  
Complex Characters

AbstractA finite group whose irreducible complex characters are rational valued is called a rational group. Thus, G is a rational group if and only if N G(〈x〉)/C G(〈x〉) ≌ Aut(〈x〉) for every x ∈ G. For example, all symmetric groups and their Sylow 2-subgroups are rational groups. Structure of rational groups have been studied extensively, but the general classification of rational groups has not been able to be done up to now. In this paper, we show that a full symmetric group of prime degree does not have any rational transitive proper subgroup and that a rational doubly transitive permutation group containing a full cycle is the full symmetric group. We also obtain several results related to the study of rational groups.

scholarly journals Factoring a group as an amalgamated free product

1973 ◽  
Vol 15 (2) ◽  
pp. 222-227 ◽  
Author(s):  
Edward T. Ordman
Keyword(s):  
Free Product ◽  
Proper Subgroup ◽  
Amalgamated Free Product ◽  
Image Position ◽  
The Cost

Even if in a decomposition of a group the Ai are completely indecomposable, there may be another decomposition with each Cj properly contained in some Ai a proper subgroup of B. The example of Bryce ([1], p. 636) may be modified, at the cost of having one Ai = B, so that I = J and Ci > Ai for all i. It is our object to study this relationship between decompositions of a group.

scholarly journals On algebra with universal finite module of differentials

1981 ◽  
Vol 83 ◽  
pp. 107-121 ◽  
Author(s):  
Norio Yamauchi
Keyword(s):  
Local Ring ◽  
Positive Characteristic ◽  
Regularity Theorem ◽  
Local Case ◽  
Finite Module ◽  
Characteristic Case ◽  
Differential Modules ◽  
Module Of Differentials

Let k be a field and A a noetherian k-algebra. In this note, we shall study the universal finite module of differentials of A over k, which is denoted by Dk(A). When the characteristic of k is zero, detailed results have been obtained by Scheja and Storch [8]. So we shall treat the positive characteristic case. In § 1, we shall study differential modules of a local ring over subfields. We obtain a criterion of regularity (Theorem (1.14)). In § 2, we shall study the formal fibres and regular locus of A with Dk(A). Our main result is Theorem (2.1) which shows that, if Dk(A) exists, then A is a universally catenary G-ring under a certain assumption. In the local case, this is a generalization of Matsumura’s theorem ([5] Theorem 15), where regularity of A is assumed.

An inverse theorem for additive bases

2016 ◽  
Vol 12 (06) ◽  
pp. 1509-1518 ◽  
Author(s):  
Yongke Qu ◽  
Dongchun Han
Keyword(s):  
Abelian Group ◽  
Proper Subgroup ◽  
Abelian Groups ◽  
Finite Abelian Group ◽  
Regular Sequence ◽  
Inverse Theorem ◽  
Additive Basis

Let [Formula: see text] be a finite abelian group of order [Formula: see text], and [Formula: see text] be the smallest prime dividing [Formula: see text]. Let [Formula: see text] be a sequence over [Formula: see text]. We say that [Formula: see text] is regular if for every proper subgroup [Formula: see text], [Formula: see text] contains at most [Formula: see text] terms from [Formula: see text]. Let [Formula: see text] be the smallest integer [Formula: see text] such that every regular sequence [Formula: see text] over [Formula: see text] of length [Formula: see text] forms an additive basis of [Formula: see text], i.e. [Formula: see text]. Recently, [Formula: see text] was determined for many abelian groups. In this paper, we determined [Formula: see text] for more abelian groups and characterize the structure of the regular sequence [Formula: see text] over [Formula: see text] of length [Formula: see text] and [Formula: see text].

scholarly journals Local Homology, Cohen–Macaulayness and Cohen–Macaulayfications

2008 ◽  
Vol 15 (01) ◽  
pp. 63-68
Author(s):  
Michael Hellus
Keyword(s):  
Local Ring ◽  
Finite Length ◽  
Necessary Condition ◽  
Direct Generalization ◽  
Local Homology ◽  
Finiteness Result ◽  
Finite Module ◽  
Noetherian Dimension

Let (R,𝔪) be a local ring, X an artinian R-module of noetherian dimension d; let x1,…,xd ∈ 𝔪 be such that 0:X (x1,…,xd)R has finite length. We show by an example that [Formula: see text] is not finite as an R-module in general; it is finite if we assume R is complete. This answers a question posed by Tang. As a first application of the latter finiteness result, we give a necessary condition for a finite module to be Cohen–Macaulay; secondly we propose a notion of Cohen–Macaulayfication and prove its uniqueness; finally we show that this new notion of Cohen–Macaulayfication is a direct generalization of a notion of Cohen–Macaulayfication introduced by Goto.

scholarly journals ON WEAKLY -SUPPLEMENTED SUBGROUPS OF SYLOW p-SUBGROUPS OF FINITE GROUPS

2011 ◽  
Vol 53 (2) ◽  
pp. 401-410 ◽  
Author(s):  
LONG MIAO
Keyword(s):  
Finite Group ◽  
Normal Subgroup ◽  
Maximal Subgroup ◽  
Finite Groups ◽  
Prime Divisor ◽  
Proper Subgroup ◽  
A Finite Group

AbstractA subgroup H is called weakly -supplemented in a finite group G if there exists a subgroup B of G provided that (1) G = HB, and (2) if H1/HG is a maximal subgroup of H/HG, then H1B = BH1 < G, where HG is the largest normal subgroup of G contained in H. In this paper we will prove the following: Let G be a finite group and P be a Sylow p-subgroup of G, where p is the smallest prime divisor of |G|. Suppose that P has a non-trivial proper subgroup D such that all subgroups E of P with order |D| and 2|D| (if P is a non-abelian 2-group, |P : D| > 2 and there exists D1 ⊴ E ≤ P with 2|D1| = |D| and E/D1 is cyclic of order 4) have p-nilpotent supplement or weak -supplement in G, then G is p-nilpotent.

scholarly journals Balanced Hermitian geometry on 6-dimensional nilmanifolds

2015 ◽  
Vol 27 (2) ◽  
Author(s):  
Luis Ugarte ◽  
Raquel Villacampa
Keyword(s):  
Proper Subgroup ◽  
Complex Structure ◽  
Holonomy Group ◽  
Hermitian Geometry

AbstractThe invariant balanced Hermitian geometry of nilmanifolds of dimension 6 is described. We prove that the (restricted) holonomy group of the associated Bismut connection reduces to a proper subgroup of SU(3) if and only if the complex structure is abelian. As an application we show that if

ON MODULES OVER GROUP RINGS OF LOCALLY SOLUBLE GROUPS WITH RANK RESTRICTIONS ON SOME SYSTEMS OF SUBGROUPS

2010 ◽  
Vol 03 (01) ◽  
pp. 45-55 ◽  
Author(s):  
O. Yu. Dashkova
Keyword(s):  
Soluble Group ◽  
Proper Subgroup ◽  
Dedekind Domain ◽  
Group Rings ◽  
Soluble Groups ◽  
Rank Restrictions ◽  
Locally Soluble Group ◽  
Dg Module

We consider a DG-module A over a Dedekind domain D. Let G be a group having infinite section p-rank (or infinite 0-rank) such that CG(A) = 1. It is known that if A is not an artinian D-module then for every proper subgroup H, the quotient A/CA(H) is an artinian D-module for every proper subgroup H of infinite section p-rank (or infinite 0-rank respectively). In this paper, it is proved that if G is a locally soluble group, then G is soluble. Some properties of soluble groups of this type are also obtained.

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