The problem of Wielandt on the existence of complements for non-abelian normal subgroups of finite groups is solved. The problem of D. K. Faddeev on the enumeration of finite biprimary groups is solved. The methods for investigation of formations of algebraic systems are developed.
Main publications:
Shemetkov L. A., “O suschestvovanii $\pi$-dopolnenii k normalnym podgruppam konechnykh grupp”, DAN SSSR, 195:1 (1970), 50–52
Shemetkov L. A., Formatsii konechnykh grupp, Nauka, 1978
Shemetkov L. A., Skiba A. N., Formatsii algebraicheskikh sistem, Nauka, Moskva, 1989
Shemetkov L. A., “On partially saturated formations and residuals of finite groups”, Comm. Algebra, 29:9 (2001), 4125–4137
A. Ballester-Bolinshe, K. Kalvo, L. A. Shemetkov, “O chastichno nasyschennykh formatsiyakh konechnykh grupp”, Matem. sb, 198:6 (2007), 3–24
