Skiba, A. N.

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ON SOME ARITHMETIC PROPERTIES OF FINITE GROUPS
A.N. Skiba
Francisk Skorina Gomel State University
104 Sovetskaya str., 246019, Gomel, Belarus
alexander.skiba49@gmail.com
We fix some partition  = fiji 2 Ig of the set of all primes P (that is, P = [i2Ii and
i \ j = ; for all i 6= j). A group G is called -primary if G is a i-group for some i = i(G).
We say that a finite group G is: -soluble if every chief factor of G is -primary; -nilpotent
if (H=K)o (G=CG(H=K)) is -primary for every chief factor H=K of G.
Based on these concepts, we develop and unify [1–5] some aspects of the theories of soluble and
quasinilpotent groups, of the subgroup lattices theory and of the theory of subnormal subgroups.
References
1. Skiba A.N. On -subnormal and -permutable subgroups of finite groups // J. Algebra. 2015. V. 436.
P. 1–16.
2. Guo W., Skiba A.N. Finite groups with generalized Ore supplement conditions for primary subgroup
// J. Algebra. 2015. V. 432. P. 205–227.
3. Skiba A.N. A generalization of a Hall theorem // J. Algebra and its Application (accepted).
4. Skiba A.N. On the generalized -Fitting subgroup of finite groups // Proc. Amer. Math. Soc.
(submitted).
5. Guo W., Skiba A.N. Finite groups with permutable complete Wielandt sets of subgroups // J. Group
Theory. 2015. V. 18. No. 2. P. 191–200.


On some arithmetic properties of finite groups

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On some arithmetic properties of finite groups

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