ieja International Electronic Journal of Algebra 1306-6048 Abdullah HARMANCI 10.24330/ieja.440221 Mathematical Sciences Matematik ODs-CHARACTERIZATION OF SOME LOW-DIMENSIONAL FINITE CLASSICAL GROUPS Akbari B. 07 05 2018 24 24 73 90 11 26 2017 Copyright © 2007, International Electronic Journal of Algebra 2007 International Electronic Journal of Algebra

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 divisorsof jGj and two distinct primes p and q are joined by an edge if andonly if there exists a solvable subgroup of G such that its order is divisibleby pq. Let p1 < p2 < < pk be all prime divisors of jGj and letDs(G) = (ds(p1); ds(p2); : : : ; ds(pk)), where ds(p) signies the degree of thevertex p in 􀀀s(G). We will simply call Ds(G) the degree pattern of solvablegraph of G. A nite group H is said to be ODs-characterizable if H = G forevery 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 nitegroup. Furthermore, we prove that the linear groups L3(q) with certain properties,are ODs-characterizable

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