Geodesic
Infinite-dimensional linear groups with restrictions on subgroups that are not soluble $A_3$-groups
Algebra i logika, Tome 46 (2007) no. 5, pp. 548-559

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We are concerned with infinite-dimensional locally soluble linear groups of infinite central dimension that are not soluble $A_3$-groups and all of whose proper subgroups, which are not soluble $A_3$-groups, have finite central dimension. The structure of groups in this class is described. The case of infinite-dimensional locally nilpotent linear groups satisfying the specified conditions is treated separately. A similar problem is solved for infinite-dimensional locally soluble linear groups of infinite fundamental dimension that are not soluble $A_3$-groups and all of whose proper subgroups, which are not soluble $A_3$-groups, have finite fundamental dimension.
Keywords: linear group, locally soluble group, minimax group, central dimension of linear group, fundamental dimension of linear group.
Mots-clés : $A_3$-group 
@article{AL_2007_46_5_a1,
     author = {O. Yu. Dashkova},
     title = {Infinite-dimensional linear groups with restrictions on subgroups that are not soluble $A_3$-groups},
     journal = {Algebra i logika},
     pages = {548--559},
     publisher = {mathdoc},
     volume = {46},
     number = {5},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2007_46_5_a1/}
}
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O. Yu. Dashkova. Infinite-dimensional linear groups with restrictions on subgroups that are not soluble $A_3$-groups. Algebra i logika, Tome 46 (2007) no. 5, pp. 548-559. http://geodesic.mathdoc.fr/item/AL_2007_46_5_a1/