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The Orbital Graph of primitive group with Socle A₇ ×A₇

Advances in Pure Mathematics 2022年第3期12卷 136-143页

作者： Jing Wu Chang Wang Jinlong Yang Hong Xu School of Preparatory Education Yunnan Minzu University Kunming China

In this paper, we mainly study the orbital graphs of primitive groups with the socle A7 x A7 which acts by diagonal action. Firstly, we calculate the element conjugate classes of A7, then we discuss the stabilizer of two points in A7. Finally, according to the relation between suborbit and orbital, we obtain the orbitals, and determine the orbital graphs.

关键词： primitive group Simple Diagonal Action Suborbit Orbital Graph

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Variables separated equations:Strikingly different roles for the Branch Cycle Lemma and the finite simple group classification

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Science China Mathematics 2012年第1期55卷 1-72页

作者： FRIED Michael D. Department of Mathematics University of California at Irvine

Davenport's Problem asks:What can we expect of two polynomials,over Z,with the same ranges on almost all residue class fields? This stood out among many separated variable problems posed by Davenport,Lewis and *** bounding the degrees,but expanding the maps and variables in Davenport's Problem,Galois stratification enhanced the separated variable theme,solving an Ax and Kochen problem from their Artin Conjecture *** and Loeser applied this to add Chow motive coefficients to previously introduced zeta functions on a diophantine *** restricting the variables,but leaving the degrees unbounded,we found the striking distinction between Davenport's problem over Q,solved by applying the Branch Cycle Lemma,and its generalization over any number field,solved by using the simple group *** encouraged Thompson to formulate the genus 0 problem on rational function monodromy *** and Thompson led its solution in *** look at two developments since the solution of Davenport's *** from MacCluer's 1967 thesis,identifying a general class of problems,including Davenport's,as monodromy precise.R(iemann)E(xistence)T(heorem)'s role as a converse to problems generalizing Davenport's,and Schinzel's (on reducibility).We use these to consider:Going beyond the simple group classification to handle imprimitive groups,and what is the role of covers and correspondences in going from algebraic equations to zeta functions with Chow motive coefficients.

关键词： group representations normal varieties Galois stratification Davenport pair Monodromy group primitive group covers fiber products Open Image Theorem Riemann's existence theorem genus zero problem

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Classification of Flag-Transitive primitive Symmetric(v, k, λ) Designs with PSL(2, q) as Socle

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Journal of Mathematical Research with Applications 2016年第2期36卷 127-139页

作者： Delu TIAN Shenglin ZHOU Department of Mathematics Guangdong University of Education School of Mathematics South China University of Technology

Let D be a nontrivial symmetric(v, k, λ) design, and G be a subgroup of the full automorphism group of D. In this paper we prove that if G acts flag-transitively, pointprimitively on D and Soc(G) = PSL(2, q), then D ... 详细信息

关键词： symmetric design flag-transitive primitive group

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