부산대학교 도서관

Let F be a field and GL n (F) the general linear group of degree n > 1 over F. The intersection graph Γ ( GL n (F)) of GL n (F) is a simple undirected graph whose vertex set includes all nontrivial proper subgroups of GL n (F). Two vertices A and B of Γ ( GL n (F)) are adjacent if A ≠ B and A ∩ B ≠ { I n }. In this paper, we show that if F is a finite field containing at least three elements, then the diameter δ (Γ ( GL n (F))) is 2 or 3. We also classify GL n (F) according to δ (Γ ( GL n (F))). In case F is infinite, we prove that Γ ( GL n (F)) is one-ended of diameter 2 and its unique end is thick. [ABSTRACT FROM AUTHOR]