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A CONDITION IN FINITE SOLVABLE GROUPS RELATED TO CYCLIC SUBGROUPS

D. IMPERATORE, MARK L. LEWIS
2010 Bulletin of the Australian Mathematical Society  
In this paper, we classify the finite 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.  ... 
doi:10.1017/s0004972710001747 fatcat:qc3hswj34jaxjeppvc3ecut5su

Cyclic partition for the groups of PSL(2,41) and PSL(2,43)

Niran Sabah, Noor Alhuda Samir Salem
2021 Al-Qadisiyah Journal Of Pure Science  
The ordinary character table and the character table (cha.ta.) 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.  ... 
doi:10.29350/qjps.2021.26.4.1351 fatcat:35dpc2carbbgxo6whjvwq3dy5q

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).  ... 

Minimal partition-free groups [article]

Afsane Bahri, Zeinab Akhlaghi, Behrooz Khosravi
2020 arXiv   pre-print
In this paper, we study a 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.  ... 
arXiv:2010.10476v1 fatcat:gdxgzsjtf5devcjc4jkiflvwfe

Intergenerational equity, efficiency, and constructibility

Luc Lauwers
2011 Economic Theory  
The Chichilnisky criterion is based upon two axioms: non dictatorship 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.  ... 
doi:10.1007/s00199-011-0603-0 fatcat:rjlqxnw6ujbxdjjnr24nuxw4oa

Intergenerational Equity, Efficiency, and Constructibility [chapter]

Luc Lauwers
2016 The Economics of the Global Environment  
The Chichilnisky criterion is based upon two axioms: non dictatorship 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.  ... 
doi:10.1007/978-3-319-31943-8_10 fatcat:2iiqlskbnjdtldfldk4hteh66u

Partitions Associated to Class Groups of Imaginary Quadratic Number Fields [article]

Kathleen Petersen, James Sellers
2021 arXiv   pre-print
Conjecturally, under an extension 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  ... 
arXiv:2111.12031v1 fatcat:se5y6oxis5hppdlohlg5garmoi

Criteria for nilpotency of groups via partitons [article]

L.J. Taghvasani, M. Zarrin
2018 arXiv   pre-print
Let G be a finite 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.  ... 
arXiv:1804.06684v1 fatcat:2gckau74qndb7ovdnt2quapfgm

On Schur Rings Over Infinite Groups [article]

Nicholas Bastian, Jaden Brewer, Andrew Misseldine
2018 arXiv   pre-print
Schur rings are a type 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.  ... 
arXiv:1806.07010v1 fatcat:l2uqsn72l5di3aadvq37g23ube

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.  ... 

On a class of solvable groups of even order

Hermann Simon
1968 Journal of Algebra  
The method is a generalization 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.  ... 
doi:10.1016/0021-8693(68)90042-2 fatcat:3o6nnchh7rbtfjc3ikwwsjb4xu

Further combinatorial constructions for optimal frequency-hopping sequences

Gennian Ge, Ryoh Fuji-Hara, Ying Miao
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 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.  ... 
doi:10.1016/j.jcta.2006.03.019 fatcat:663deipeabgjnapcuxrksjysfe

Combinatorial enumeration of cyclic covers of P1

Alberto BESANA, Cristina MARTINEZ
2018 Turkish Journal of Mathematics  
Acknowledgments We would like to thank Fei Xu and Vivek Mallick for interesting discussions during the preparation 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 .  ... 
doi:10.3906/mat-1610-84 fatcat:nryyxj363zdkvpt2fo37lsqzbe

A note on finite C-tidy groups

Sekhar Jyoti Baishya
2013 International Journal of Group Theory  
Let $G$ be a 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.  ... 
doaj:ef27b183a13640d586d6b5af5b4b63c5 fatcat:4r7nzyr2bfhorjp57gsrxrwysi

The Conrad Program: From ℓ -groups to algebras of logic

Michal Botur, Jan Kühr, Lianzhen Liu, Constantine Tsinakis
2016 Journal of Algebra  
The present article demonstrates that large parts 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).  ... 
doi:10.1016/j.jalgebra.2015.10.015 fatcat:nbujserrd5dhvlalxhc27eddja
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