882 research outputs found
Classification and properties of the -submaximal subgroups in minimal nonsolvable groups
Let be a set of primes. According to H. Wielandt, a subgroup of a
finite group is called a -submaximal subgroup if there is a
monomorphism into a finite group such that
is subnormal in and for a -maximal subgroup
of . In his talk at the well-known conference on finite groups in Santa-Cruz
(USA) in 1979, Wielandt posed a series of open questions and among them the
following problem: to describe the -submaximal subgroup of the minimal
nonsolvable groups and to study properties of such subgroups: the pronormality,
the intravariancy, the conjugacy in the automorphism group etc. In the article,
for every set of primes, we obtain a description of the -submaximal
subgroup in minimal nonsolvable groups and investigate their properties, so we
give a solution of Wielandt's problem
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