### On finite same-invariant linear groups.

Kushpel', N.N. (2005)

Journal of Mathematical Sciences (New York)

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Kushpel', N.N. (2005)

Journal of Mathematical Sciences (New York)

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Let F be a field, A be a vector space over F, GL(F, A) be 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 dim F(B/Core G(B)) is finite. In the current article, we study linear groups G such that every subspace of A is either nearly G-invariant or almost G-invariant in the case when G is a soluble p-group where p = char F.