Literature Cited
S. A. Chunikhin, Sets of nonspecial subgroups and the p-nilpotency of finite groups, Doklady Ak. nauk SSSR,118, No. 4 (1958), pp. 654–656.
V. I. Sergienko, Saturation of finite groups of solvable nonspecial subgroups, Sib. matem zh.,4, No. 4 (1963), pp. 926–934.
V. I. Sergienko, Classes and complexions of subgroups of finite groups, Doklady Ak. nauk SSSR,146, No. 6 (1962), pp. 1279–1281.
Ya. G. Berkovich, Characterization of certain classes of finite groups, Doklady Ak. nauk SSSR,151, No. 5 (1963), pp. 1007–1009.
Ya. G. Berkovich, Certain criteria of the solvability of finite groups, Sib. matem. zh.,4, (1963), pp. 723–728
S. A. Chunikhin, The π-properties of finite groups, Matem. sb.,25, No. 3 (1949), pp. 321–346.
S. A. Chunikhin, Sylow properties of finite groups, Doklady Ak. nauk SSSR,73, No. 1 (1950), pp. 29–32.
J. G. Thompson, Normal p-complements for finite groups, Math. Zeits.,72, (1960), pp. 332–354.
W. Burnside, Theory of groups of finite order, Dover Publications, New York (1955).
P. Hall, A note on soluble groups, J. London Math. Soc., 3 (1928), pp. 98–105.
S. A. Chunikhin, Decomposition of π-solvable groups into a direct product of subgroups, Doklady Ak. nauk SSSR,147, No. 5 (1962), pp. 1042–1044.
W. Feit and J. G. Thompson, Solvability of groups of odd order, Pacific J. Math.,13, No. 3 (1963), pp. 775–1029.
S. A. Chunikhin, Existence of subgroups of a finite group, Proceedings of the Seminar on Group Theory [in Russian], Moscow (1938), pp. 106–125.
O. Yu. Shmidt, Groups, all subgroups of which are special, Matem. sb., 31 (1924), pp. 366–372.
L. E. Dickson, Linear groups with an exposition of Galois field theory, Leipzig, 1901.
I. K. Chunikhina and S. A. Chunikhin, On p-decomposable groups, Matem. sb. 15, No. 4 (1944). pp. 325–342.
J. G. Thompson, Finite groups with fixed point-free automorphisms of prime order, Proc. Nat. Acad. Sci., 45, No. 4 (1959), pp. 578–581.
Z. Janko, Verallgemeinerung eines Satzes von B. Huppert und J. G. Thompson [Generalization of a theorem of B. Huppert and J. G. Thompson], Arch. Math.,12 (1961), pp. 280–281.
J. L. Alperin, A special class of regular p-groups, Trans. Amer. Math. Soc.,106, No. 1 (1963), pp. 77–99.
S. A. Chunikhin, Factorization of finite groups, Matem. sb., 39, No. 4 (1956), pp. 465–490.
H. Hasse, Lectures on the Theory of Numbers, IL, Moscow (1955).
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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 7, No. 1, pp. 206–211, January–February, 1966
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Berkovich, Y.G. Existence of nonlilpotent solvable subgroups of a finite unsolvable group. Sib Math J 7, 167–170 (1966). https://doi.org/10.1007/BF00967826
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DOI: https://doi.org/10.1007/BF00967826