ON RECOGNITION OF FINITE SIMPLE GROUPS BY ORDER AND DEGREE PATTERN OF SOLVABLE GRAPH

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AKBARI B.; Iiyori N.; MOGHADDAMFAR A.R.

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Seminar Paper

Paper Information

Seminar: IRANIAN ALGEBRA SEMINAR
Year:2016 | Issue:25

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Title

ON RECOGNITION OF FINITE SIMPLE GROUPS BY ORDER AND DEGREE PATTERN OF SOLVABLE GRAPH

Author(s)

AKBARI B. | Iiyori N. | MOGHADDAMFAR A.R.

Keywords

SOLVABLE GRAPH

DEGREE PATTERN

SIMPLE GROUP

ODS-CHARACTERIZATION OF A FINITE GROUP

Abstract

THE SOLVABLE GRAPH OF A FINITE GROUPG, DENOTED BY GS (G), IS A SIMPLE GRAPH WHOSE VERTICES ARE THE PRIME DIVISORS OF|G| AND TWO DISTINCT PRIMES P AND Q ARE JOINED BY AN EDGE IF AND ONLY IF THERE EXISTS A SOLVABLE SUBGROUP OFG SUCH THAT ITS ORDER IS DIVISIBLE BY PQ. LET P1 < P2 < · · · <PK BE ALL PRIME DIVISORS OF |G| AND LET DS(G) = (DS (P1), DS (P2), ..., DS (PK)), WHERE DS(P) SIGNIFIES THE DEGREE OF THE VERTEXP IN GS(G). WE WILL SIMPLY CALL DS(G) THE DEGREE PATTERN OF SOLVABLE GRAPH OF G. THE PURPOSE OF THIS ARTICLE IS TWOFOLD. FIRST, IT PROVIDES THE STRUCTURE OF ANY FINITE GROUP G (UP TO ISOMORPHISM) FOR WHICH GS(G) IS STAR OR BIPARTITE. SECOND, IT IS PROVED THAT THE SPORADIC SIMPLE GROUPS AND SOME OF PROJECTIVE SPECIAL LINEAR GROUPS L2(Q) ARE CHARACTERIZED VIA ORDER AND DEGREE PATTERN OF SOLVABLE GRAPHS.

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APA: Copy

AKBARI, B., Iiyori, N., & MOGHADDAMFAR, A.R.. (2016). ON RECOGNITION OF FINITE SIMPLE GROUPS BY ORDER AND DEGREE PATTERN OF SOLVABLE GRAPH. IRANIAN ALGEBRA SEMINAR. SID. https://sid.ir/paper/938533/en

Vancouver: Copy

AKBARI B., Iiyori N., MOGHADDAMFAR A.R.. ON RECOGNITION OF FINITE SIMPLE GROUPS BY ORDER AND DEGREE PATTERN OF SOLVABLE GRAPH. 2016. Available from: https://sid.ir/paper/938533/en

IEEE: Copy

B. AKBARI, N. Iiyori, and A.R. MOGHADDAMFAR, “ON RECOGNITION OF FINITE SIMPLE GROUPS BY ORDER AND DEGREE PATTERN OF SOLVABLE GRAPH,” presented at the IRANIAN ALGEBRA SEMINAR. 2016, [Online]. Available: https://sid.ir/paper/938533/en

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