Geodesic
The representation image unipotency of the group $F_2$ by mapping primitive elements into unipotent matrices with small Jordan blocks
Problemy fiziki, matematiki i tehniki, no. 3 (2011), pp. 81-83.

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

It is proved that the representation image of the free group $F_2(x, y)$ in $GL(n, C))$ is an unipotent subgroup, when $(\rho (p) - E)^5 = 0$ for all primitive elements $p$ and $(\rho(\xi) - E)^2 = 0$, $(\rho(\gamma) - E)^3 = 0$ for some associated primitive elements $\xi$ and $\gamma$ of the group $F_2$ .
Keywords: unipotent subgroup, primitive element, representation of group. 
@article{PFMT_2011_3_a13,
     author = {O. I. Tavgen' and D. Junhua and L. Chunyan},
     title = {The representation image unipotency of the group $F_2$ by mapping primitive elements into unipotent matrices with small {Jordan} blocks},
     journal = {Problemy fiziki, matematiki i tehniki},
     pages = {81--83},
     publisher = {mathdoc},
     number = {3},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/PFMT_2011_3_a13/}
}
TY  - JOUR
AU  - O. I. Tavgen'
AU  - D. Junhua
AU  - L. Chunyan
TI  - The representation image unipotency of the group $F_2$ by mapping primitive elements into unipotent matrices with small Jordan blocks
JO  - Problemy fiziki, matematiki i tehniki
PY  - 2011
SP  - 81
EP  - 83
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PFMT_2011_3_a13/
LA  - ru
ID  - PFMT_2011_3_a13
ER  - 
%0 Journal Article
%A O. I. Tavgen'
%A D. Junhua
%A L. Chunyan
%T The representation image unipotency of the group $F_2$ by mapping primitive elements into unipotent matrices with small Jordan blocks
%J Problemy fiziki, matematiki i tehniki
%D 2011
%P 81-83
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PFMT_2011_3_a13/
%G ru
%F PFMT_2011_3_a13
O. I. Tavgen'; D. Junhua; L. Chunyan. The representation image unipotency of the group $F_2$ by mapping primitive elements into unipotent matrices with small Jordan blocks. Problemy fiziki, matematiki i tehniki, no. 3 (2011), pp. 81-83. http://geodesic.mathdoc.fr/item/PFMT_2011_3_a13/

[1] V. Magnus, A. Karras, D. Soliter, Kombinatornaya teoriya grupp: predstavlenie grupp v terminakh obrazuyuschikh i sootnoshenii, Nauka, M., 1974 | MR | Zbl

[2] Yu. B. Samsonov, O. I. Tavgen, “Unipotentnost obraza predstavleniya $F_2(x,y)$ matritsami iz $GL(n,C)$, $n=2,3,4$, pri uslovii otobrazheniya obrazuyuschikh i primitivnykh elementov v unipotentnye matritsy”, Doklady NAN Belarusi, 45:6 (2001), 29–32 | MR | Zbl

[3] O. I. Tavgen, Yan Sinsun, “Unipotentnost obraza predstavleniya $F_2(x,y)$ v $GL(5,\mathbb{C})$ pri otobrazhenii primitivnykh elementov v unipotentnye matritsy”, Vestnik BGU. Seriya 1, 2009, no. 3, 74–79 | MR | Zbl

[4] O. I. Tavgen, Yan Sinsun, “Unipotentnost obraza predstavleniya $F_2(x,y)$ v $GL(n,C)$ pri uslovii otobrazheniya primitivnykh elementov v unipotentnye matritsy s kletkami Zhordana malykh razmernostei”, Vesnik VDU. Seryya 1, 2010, no. 3 (57), 48–53

[5] O. I. Tavgen, Yan Sinsun, Lyu Sschunyan, “Unipotentnost obraza predstavleniya $F_2$ v $GL(n,C)$ pri otobrazhenii primitivnykh elementov v unipotentnye matritsy s kletkami Zhordana maloi razmernosti, II”, Vesnik VDU. Seryya 1, 2010, no. 6 (60), 11–14