# On some infinite dimensional linear groups

Leonid Kurdachenko; Alexey Sadovnichenko; Igor Subbotin

Open Mathematics (2009)

- Volume: 7, Issue: 2, page 176-185
- ISSN: 2391-5455

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topLeonid Kurdachenko, Alexey Sadovnichenko, and Igor Subbotin. "On some infinite dimensional linear groups." Open Mathematics 7.2 (2009): 176-185. <http://eudml.org/doc/269113>.

@article{LeonidKurdachenko2009,

abstract = {Let F be a field, A be a vector space over F, and GL(F,A) the group of all automorphisms of the vector space A. A subspace B of A is called nearly G-invariant, if dimF(BFG/B) is finite. A subspace B is called almost G-invariant, if dimF(B/CoreG(B)) is finite. In the present article we begin the study of subgroups G of GL(F,A) such that every subspace of A is either nearly G-invariant or almost G-invariant. More precisely, we consider the case when G is a periodic p′-group where p = charF.},

author = {Leonid Kurdachenko, Alexey Sadovnichenko, Igor Subbotin},

journal = {Open Mathematics},

keywords = {Vector space; Linear groups; Periodic groups; Invariant subspace; infinite-dimensional linear groups; periodic groups; soluble groups},

language = {eng},

number = {2},

pages = {176-185},

title = {On some infinite dimensional linear groups},

url = {http://eudml.org/doc/269113},

volume = {7},

year = {2009},

}

TY - JOUR

AU - Leonid Kurdachenko

AU - Alexey Sadovnichenko

AU - Igor Subbotin

TI - On some infinite dimensional linear groups

JO - Open Mathematics

PY - 2009

VL - 7

IS - 2

SP - 176

EP - 185

AB - Let F be a field, A be a vector space over F, and GL(F,A) the group of all automorphisms of the vector space A. A subspace B of A is called nearly G-invariant, if dimF(BFG/B) is finite. A subspace B is called almost G-invariant, if dimF(B/CoreG(B)) is finite. In the present article we begin the study of subgroups G of GL(F,A) such that every subspace of A is either nearly G-invariant or almost G-invariant. More precisely, we consider the case when G is a periodic p′-group where p = charF.

LA - eng

KW - Vector space; Linear groups; Periodic groups; Invariant subspace; infinite-dimensional linear groups; periodic groups; soluble groups

UR - http://eudml.org/doc/269113

ER -

## References

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- [7] Muñoz-Escolano J.M., Otal J., Semko N.N., Periodic linear groups with the weak chain conditions on subgroups of infinite central dimension, Comm. Algebra, 2008, 36, 749–763 http://dx.doi.org/10.1080/00927870701724318[WoS][Crossref] Zbl1141.20030
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- [10] Wehrfritz B.A.F., Infinite linear groups, Springer, Berlin, 1973

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