This article is cited in 2 papers

Infinite-dimensional linear groups with restrictions on subgroups that are not soluble $A_3$-groups

O. Yu. Dashkova


Abstract: 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, $A_3$-group, central dimension of linear group, fundamental dimension of linear group.

UDC: 512.544

Received: 17.08.2006
Revised: 26.04.2007

 English version: Algebra and Logic, 2007, 46:5, 297–302

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