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A CONDITION IN FINITE SOLVABLE GROUPS RELATED TO CYCLIC SUBGROUPS

2010
*
Bulletin of the Australian Mathematical Society
*

In this paper, we classify the finite

doi:10.1017/s0004972710001747
fatcat:qc3hswj34jaxjeppvc3ecut5su
*groups*belonging to the class*of**cyclic*-transitive*groups*. ... A*group*G is said to be*cyclic*-transitive if the following condition holds: if x, y, z are nonidentity elements*of*G such that x, y and y, z are both*cyclic*, then x, z is also*cyclic*. 2000 Mathematics ... Suppose that there exists a*partition**F**of*G. Then G is*cyclic*-transitive if and only if every subgroup*of**F*is*cyclic*-transitive. PROOF. Suppose that every subgroup*of**F*is*cyclic*-transitive. ...##
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Cyclic partition for the groups of PSL(2,41) and PSL(2,43)

2021
*
Al-Qadisiyah Journal Of Pure Science
*

The ordinary character table and the character table (cha.ta.)

doi:10.29350/qjps.2021.26.4.1351
fatcat:35dpc2carbbgxo6whjvwq3dy5q
*of*rational representations (ra.repr.) for projective special linear*groups*(2,41) and (2,43) find in this work to find the*cyclic**partition*... for each*group*... Author in [6] proved that for any*cyclic*P-*group*G, K(G) = Zp and K(G) = 1 Z i n P i for any*cyclic**group*G*of*order P n . 2-Base for the (n,*F*) In this section we display some notions. ...##
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Page 440 of American Journal of Mathematics Vol. 49, Issue 3
[page]

1927
*
American Journal of Mathematics
*

*F*.’s

*of*the

*cyclic*

*groups*are

*of*considerable theoretical as well as practical importance. ...

*F*.

*of*a dihedral

*group*derived from a transitive

*cyclic*

*group*:

*of*degree w will be denoted by Dih(w). ...

##
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Minimal partition-free groups
[article]

2020
*
arXiv
*
pre-print

In this paper, we study a

arXiv:2010.10476v1
fatcat:gdxgzsjtf5devcjc4jkiflvwfe
*partition*-free*group*G whose all proper non-*cyclic*subgroups admit non-trivial*partitions*. ... We call a*group*G that does not admit any non-trivial*partition*a*partition*-free*group*. ... Obviously,*cyclic**groups*do not admit a non-trivial*partition*. We call a non-*cyclic**group*that does not admit a non-trivial*partition*, a*partition*-free*group*or briefly a PF-*group*. ...##
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Intergenerational equity, efficiency, and constructibility

2011
*
Economic Theory
*

The Chichilnisky criterion is based upon two axioms: non dictatorship

doi:10.1007/s00199-011-0603-0
fatcat:rjlqxnw6ujbxdjjnr24nuxw4oa
*of*the present and non dictatorship*of*the future. Here, the very long run is captured by a finitely additive measure. ... I show that a maximal anonymity axiom compatible with Pareto is a non-constructible object; its existence relies on the Axiom*of*Choice. ... Anonymity demands are formulated in terms*of**groups**of**cyclic*permutations. We focussed on*partition**groups**of**cyclic*permutations. ...##
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Intergenerational Equity, Efficiency, and Constructibility
[chapter]

2016
*
The Economics of the Global Environment
*

The Chichilnisky criterion is based upon two axioms: non dictatorship

doi:10.1007/978-3-319-31943-8_10
fatcat:2iiqlskbnjdtldfldk4hteh66u
*of*the present and non dictatorship*of*the future. Here, the very long run is captured by a finitely additive measure. ... I show that a maximal anonymity axiom compatible with Pareto is a non-constructible object; its existence relies on the Axiom*of*Choice. ... Anonymity demands are formulated in terms*of**groups**of**cyclic*permutations. We focussed on*partition**groups**of**cyclic*permutations. ...##
###
Partitions Associated to Class Groups of Imaginary Quadratic Number Fields
[article]

2021
*
arXiv
*
pre-print

Conjecturally, under an extension

arXiv:2111.12031v1
fatcat:se5y6oxis5hppdlohlg5garmoi
*of*the Cohen and Lenstra heuristics by Holmin et. al., these*partitions*correspond to abelian p-*groups*that appear as class*groups**of*imaginary quadratic number fields ... We investigate properties*of*attainable*partitions**of*integers, where a*partition*(n_1,n_2, ..., n_r)*of*n is attainable if ∑ (3-2i)n_i≥ 0. ... When G is an abelian*group**of*odd order, this can be stated as*F*(G) ≈ P (G)*F*(|G|) where*F*(G) and*F*(h) are the number*of*fundamental discriminants whose associated class*group*is G, and class number ...##
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Criteria for nilpotency of groups via partitons
[article]

2018
*
arXiv
*
pre-print

Let G be a finite

arXiv:1804.06684v1
fatcat:2gckau74qndb7ovdnt2quapfgm
*group*and S< G. A cover for a*group*G is a collection*of*subgroups*of*G whose union is G. We use the term n-cover for a cover with n members. ... ., H_n} is said to be a strict S-*partition**of*G if H_i∩ H_j= S for i≠ j and Π is said an equal strict S-*partition*(or ES-*partition*)*of*G, if Π is a strict S-*partition*and |H_i|=|H_j| for all i≠ j. ... If G is a finite*group*with odd order and*F*is a nontrivial subgroup*of*G. Then every proper non-*cyclic*subgroup*of*G has an EF -*partition*if and only if G is minimal non-*cyclic**group*. ...##
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On Schur Rings Over Infinite Groups
[article]

2018
*
arXiv
*
pre-print

Schur rings are a type

arXiv:1806.07010v1
fatcat:l2uqsn72l5di3aadvq37g23ube
*of*subring*of*the*group*ring that is spanned by a*partition**of*the*group*that meets certain conditions. Past literature has exclusively focused on the finite*group*case. ... This paper extends many classic results about Schur rings to the infinite*groups*, including Leung-Man's classification*of*Schur rings over finite*cyclic**groups*. ... The*group*ring*F*[G] itself forms a Schur ring over G for any*group*, whose*partition*corresponds to singletons*of**group*elements. ...##
###
Page 353 of American Mathematical Society. Transactions of the American Mathematical Society Vol. 30, Issue 2
[page]

1928
*
American Mathematical Society. Transactions of the American Mathematical Society
*

1928] PRIMITIVE

*GROUPS*353 order 168. Then if J; exists, J/ is intransitive with two*cyclic*constituents*of*degree 3 each. Now*F*is*of*degree 7p+6. ... Since the J*group**of*the constituent*of*degree 4+3 must be*cyclic*, all the*partitions*which bring a transposition into it are impossible. ...##
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On a class of solvable groups of even order

1968
*
Journal of Algebra
*

The method is a generalization

doi:10.1016/0021-8693(68)90042-2
fatcat:3o6nnchh7rbtfjc3ikwwsjb4xu
*of*the concept*of*a*partition*: Let S be a set*of*subgroups*of*a*group*G and T a subgroup*of*G. ... There can certainly be no influence on G if T and S are small: e.g., let T be a*cyclic*subgroup*of*G*of*order a prime and S contains only T; here S induces the trivial*partition*on T and there is no influence ... Hence all Sylow*groups**of*K are*cyclic*and K, as the direct product*of*its Sylow*groups*, is itself*cyclic*and hence M is dihedral. ...##
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Further combinatorial constructions for optimal frequency-hopping sequences

2006
*
Journal of combinatorial theory. Series A
*

Theory 50 (2004) 2408-2420] from a combinatorial approach, where a correspondence between frequency-hopping (FH) sequences and

doi:10.1016/j.jcta.2006.03.019
fatcat:663deipeabgjnapcuxrksjysfe
*partition*-type*cyclic*difference packings was established, and several combinatorial ... As a consequence, more new infinite series*of*optimal FH sequences are obtained. ... Xiang at the University*of*Delaware and Professor L. ...##
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Combinatorial enumeration of cyclic covers of P1

2018
*
Turkish Journal of Mathematics
*

Acknowledgments We would like to thank Fei Xu and Vivek Mallick for interesting discussions during the preparation

doi:10.3906/mat-1610-84
fatcat:nryyxj363zdkvpt2fo37lsqzbe
*of*the work and Joachim Kock for reading the paper and some useful comments. ... Let*F*0 be the fixed field*F*µ d by the action*of*the*cyclic**group*ξ d . ... Let q = p n and consider the Galois extension*F*q /*F*p with Galois*group*the*cyclic**group**of*order n . ...##
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A note on finite C-tidy groups

2013
*
International Journal of Group Theory
*

Let $G$ be a

doaj:ef27b183a13640d586d6b5af5b4b63c5
fatcat:4r7nzyr2bfhorjp57gsrxrwysi
*group*and $x in G$. The*cyclicizer**of*$x$ is defined to be the subset $Cyc(x)={ y in G | is*cyclic*}. $G$ is said to be a tidy*group*if $Cyc(x)$ is a subgroup for all $x in G$. ... We call $G$ to be a C-tidy*group*if $Cyc(x)$ is a*cyclic*subgroup for all $x in G setminus K(G)$, where $K(G)$ is the intersection*of*all the*cyclicizers*in $G$. ... By Proposition 2.1, Π is a non-trivial*partition**of*G. Now, by a result*of*Kegel [12] , the fitting subgroup*F*(G) is*cyclic*normal*of*prime index p. ...##
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The Conrad Program: From ℓ -groups to algebras of logic

2016
*
Journal of Algebra
*

The present article demonstrates that large parts

doi:10.1016/j.jalgebra.2015.10.015
fatcat:nbujserrd5dhvlalxhc27eddja
*of*the Conrad Program can be profitably extended in the setting*of*e-*cyclic*residuated lattices. ... A number*of*research articles have established the significant role*of*lattice-ordered*groups*(l-*groups*) in logic. ... Let L be a semilinear e-*cyclic*RL, and let C, D be*partitions**of*the Boolean algebra B(L). ...
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