Geodesic
On finite groups in which every subgroup is either $\mathfrak{F}$-subnormal or $\mathfrak{F}$-abnormal
Problemy fiziki, matematiki i tehniki, no. 2 (2015), pp. 72-74.

Voir la notice de l'article provenant de la source Math-Net.Ru

The structure of finite groups in which every proper subgroup is either $\mathfrak{F}$-subnormal or $\mathfrak{F}$-abnormal, where $\mathfrak{F}$ is a saturated hereditary formation with the Shemetkov property containing all nilpotent groups is studied. In particular, descriptions of these groups in the cases when $\mathfrak{F}$ is either the formation of all $p$-nilpotent groups or all $p$-decomposable groups were obtained.
Keywords: finite group, $\mathfrak{F}$-subnormal subgroup, $\mathfrak{F}$-abnormal subgroup, saturated formation, formation with the Shemetkov property. 
@article{PFMT_2015_2_a11,
     author = {V. N. Semenchuk and A. N. Skiba},
     title = {On finite groups in which every subgroup is either $\mathfrak{F}$-subnormal or $\mathfrak{F}$-abnormal},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {72--74},
     publisher = {mathdoc},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2015_2_a11/}
}
TY  - JOUR
AU  - V. N. Semenchuk
AU  - A. N. Skiba
TI  - On finite groups in which every subgroup is either $\mathfrak{F}$-subnormal or $\mathfrak{F}$-abnormal
JO  - Problemy fiziki, matematiki i tehniki
PY  - 2015
SP  - 72
EP  - 74
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PFMT_2015_2_a11/
LA  - ru
ID  - PFMT_2015_2_a11
ER  - 
%0 Journal Article
%A V. N. Semenchuk
%A A. N. Skiba
%T On finite groups in which every subgroup is either $\mathfrak{F}$-subnormal or $\mathfrak{F}$-abnormal
%J Problemy fiziki, matematiki i tehniki
%D 2015
%P 72-74
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PFMT_2015_2_a11/
%G ru
%F PFMT_2015_2_a11
V. N. Semenchuk; A. N. Skiba. On finite groups in which every subgroup is either $\mathfrak{F}$-subnormal or $\mathfrak{F}$-abnormal. Problemy fiziki, matematiki i tehniki, no. 2 (2015), pp. 72-74. http://geodesic.mathdoc.fr/item/PFMT_2015_2_a11/

[1] A. Fattachi, “Groups with only normal and abnormal subgroups”, J. Algebra, 28:1 (1974), 15–19 | MR

[2] G. Ebert, S. Bauman, “A note on subnormal and abnormal chains”, J. Algebra, 36:2 (1975), 287–293 | MR | Zbl

[3] P. Förster, “Finite groups all of whose subgroups are $\mathfrak{F}$-subnormal or $\mathfrak{F}$-subabnormal”, J. Algebra, 1986, no. 1, 285–293 | MR | Zbl

[4] V. N. Semenchuk, “Stroenie konechnykh grupp s $\mathfrak{F}$-abnormalnymi ili $\mathfrak{F}$-subnormalnymi podgruppami”, Voprosy algebry, 2, Izd-vo «Universitetskoe», Minsk, 1986, 50–55

[5] V. N. Semenchuk, S. N. Shevchuk, “Konechnye gruppy, u kotorykh primarnye podgruppy libo $\mathfrak{F}$-subnormalny, libo $\mathfrak{F}$-abnormalny”, Izvestiya vuzov. Matematika, 2011, no. 8, 46–55

[6] V. N. Semenchuk, A. N. Skiba, On one generalization of finite $\mathfrak{U}$-critical groups, arXiv: 1412.5469v1 [math.GR]

[7] L. A. Shemetkov, Formatsii konechnykh grupp, Nauka, M., 1978, 267 pp. | MR

[8] N. Ito, “Note on (LM)-groups of finite order”, Kodai Math. Sem. Rep., 1–2 (1951), 1–6 | MR | Zbl

[9] I. K. Chunikhina, S. A. Chunikhin, “O $p$-razlozhimykh gruppakh”, Mat. sbornik, 15(57):2 (1944), 325–342 | MR | Zbl

[10] S. N. Shevchuk, V. N. Semenchuk, “Konechnye gruppy s obobschenno abnormalnymi podgruppami”, Problemy fiziki, matematiki i tekhniki, 2010, no. 4(5), 57–60

[11] W. Willems, “On the projectives of a group algebra”, Math. Z., 171 (1980), 163–174 | MR | Zbl