Problems in group theory - Stewart, W (1967)
Using combinatorial and character-theoretic methods the following theorems are proved. Theorem I Let G be a finite simple group containing two non-conjugate subgroups A, B such that: if a ε A, a &notequals; 1, then CG (a) = A; if b ε B, b &notequals; 1, then CG(b) = B; | NG(A)/A | = 2, | NG(B)/B | = 2. Then G is isomorphic to some PSL (2,2a). Theorem II Let G be a finite simple group containing a subgroup A such that: if a ε A, a &notequals; 1, then CG(a) = A; | NG(A)/A | = 2; 3 divides | A | . Then G is isomorphic to some PSL (2,q).