Geodesic
On $TI$-subgroups of finite groups
Izvestiya. Mathematics , Tome 28 (1987) no. 1, pp. 21-35.

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

The author studies the normal closure in a finite group of an elementary $2$-subgroup $A$ which is a $TI$-subgroup, and which satisfies the following condition: for an arbitrary collection $A_1,A_2,\dots,A_k$ ($k\geqslant2$) of distinct commuting subgroups conjugate to $A$, the product $A_2\dots A_k$ does not contain $A_1$. Bibliography: 17 titles. 
@article{IM2_1987_28_1_a1,
     author = {A. A. Makhnev},
     title = {On $TI$-subgroups of finite groups},
     journal = {Izvestiya. Mathematics },
     pages = {21--35},
     publisher = {mathdoc},
     volume = {28},
     number = {1},
     year = {1987},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1987_28_1_a1/}
}
TY  - JOUR
AU  - A. A. Makhnev
TI  - On $TI$-subgroups of finite groups
JO  - Izvestiya. Mathematics 
PY  - 1987
SP  - 21
EP  - 35
VL  - 28
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1987_28_1_a1/
LA  - en
ID  - IM2_1987_28_1_a1
ER  - 
%0 Journal Article
%A A. A. Makhnev
%T On $TI$-subgroups of finite groups
%J Izvestiya. Mathematics 
%D 1987
%P 21-35
%V 28
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1987_28_1_a1/
%G en
%F IM2_1987_28_1_a1
A. A. Makhnev. On $TI$-subgroups of finite groups. Izvestiya. Mathematics , Tome 28 (1987) no. 1, pp. 21-35. http://geodesic.mathdoc.fr/item/IM2_1987_28_1_a1/

[1] Makhnev A. A., “Ob elementarnykh $TI$-podgruppakh v konechnykh gruppakh”, Matem. zametki, 30:2 (1981), 179–184 | MR | Zbl

[2] Makhnev A. A., O podgruppakh nekornevogo tipa v konechnykh gruppakh, dep. v VINITI 8.04.82, No 1673–82 Dep., Inst. matem. i mekhaniki UNTs AN SSSR, Sverdlovsk, 1982, 34 pp.

[3] Aschbacher M., “Finite groups generated by odd transpositions”, Math. Z., 127:1 (1972), 45–46 ; J. Algebra, 26:3 (1973), 451–491 | DOI | MR | DOI | MR

[4] Aschbacher M., “Tightly embedded subgroups of finite groups”, J. Algebra, 42:1 (1976), 85–101 | DOI | MR | Zbl

[5] Aschbacher M., “On finite groups of component type”, Illinois J. Math., 19:1 (1975), 87–115 | MR | Zbl

[6] Aschbacher M., “Thin finite simple groups”, J. Algebra, 54:1 (1978), 50–152 | DOI | MR | Zbl

[7] Aschbacher M., “Weak closure in finite groups of even characteristic”, J. Algebra, 70:2 (1981), 561–627 | DOI | MR | Zbl

[8] Fischer B., “Finite groups generated by 3-transpositions”, Invent. Math., 13:3 (1971), 232–246 | DOI | MR | Zbl

[9] Foote R., “Component type theorems for finite groups in characteristic 2”, Illinois J. Math., 26:1 (1982), 62–111 | MR | Zbl

[10] Foote R., Harris M., “Tightly embedded subgroups with cores”, Arch, der Math., 38:6 (1982), 481–490 | DOI | MR | Zbl

[11] Gorenstein D,, Harada K., “On finite groups with Sylow 2-subgroups of type $A_n$, $n=8, 9, 10, 11$”, Math. Z., 117:1–4 (1970), 207–238 | DOI | MR | Zbl

[12] Timmesfeld F., “Groups generated by root-involutions”, J. Algebra, 33:1 (1975), 75–134 ; 35:1–3, 367–441 | DOI | MR | Zbl | Zbl

[13] Timmesfeld F., “Groups with weakly closed $TI$-subgroups”, Math. Z., 141:3 (1975), 243–278 | DOI | MR

[14] Timmesfeld F., “On elementary abelian $TI$-subgroups”, J. Algebra, 44:2 (1977), 457–476 | DOI | MR | Zbl

[15] Timmesfeld F., “A condition for the existence of a weakly closed $TI$-set”, J. Algebra, 60:2 (1979), 472–484 | DOI | MR | Zbl

[16] Timmesfeld F., “Finite simple groups in which the generalized Fitting group of centralizer of some involution is extraspecial”, Ann. Math., 107:2 (1978), 297–369 | DOI | MR | Zbl

[17] Timmesfeld F., “On finite groups in which a maximal abelian normal subgroup of some maximal 2-local subgroup is a $TI$-set”, Proc. London Math. Soc.(3), 43:1 (1981), 1–45 | DOI | MR | Zbl