ODs-CHARACTERIZATION OF SOME LOW-DIMENSIONAL FINITE CLASSICAL GROUPS

Year 2018, Volume: 24 Issue: 24, 73 - 90, 05.07.2018

B. Akbari

https://doi.org/10.24330/ieja.440221

Abstract

The solvable graph of a nite group G, which is denoted by

􀀀s(G), is a simple graph whose vertex set is comprised of the prime divisors

of jGj and two distinct primes p and q are joined by an edge if and

only if there exists a solvable subgroup of G such that its order is divisible

by pq. Let p1 < p2 < < pk be all prime divisors of jGj and let

Ds(G) = (ds(p1); ds(p2); : : : ; ds(pk)), where ds(p) signies the degree of the

vertex p in 􀀀s(G). We will simply call Ds(G) the degree pattern of solvable

graph of G. A nite group H is said to be ODs-characterizable if H = G for

every nite group G such that jGj = jHj and Ds(G) = Ds(H). In this paper,

we study the solvable graph of some subgroups and some extensions of a nite

group. Furthermore, we prove that the linear groups L3(q) with certain properties,

are ODs-characterizable

Keywords

Solvable graph, degree pattern, simple group, local subgroup

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