On the solvability and factorization of some $\pi$-solvable irreducible linear groups of primary degree. Part III

The article is the third one in a series of papers, where for a set $\pi$ consisting of odd primes, finite $\pi$-solvable irreducible complex linear groups of degree $2|H|+1$ are investigated, for which Hall $\pi$-subgroups are $TI$-subgroups and are not normal in groups. The purpose of the series is to prove solvability and to determine the conditions for factorization of such groups. The proof of the theorem is continued. Further properties of the minimal counterexample to the theorem are established.