Title: A STRUCTURE THEOREM OF SOLVABLE SEMISIMPLX GROUPS
Abstract: Definition: we call P a prime normal subgroup of G, if P is the normal subgroups of G such that, for any normal subgroups A and B of G, [A,B]≤P implies A≤P or B≤P.We call group G a prime group if {e} is a prime normal subgroup of G, where e is the unity of G.Definition, A group G is solvable semisimpla, if G possesses no nontrivial solvable normar subgroups. Theorem: Suppose G is a solvable-semisimple, then the intersection of all prime normal subgroups of G is{e}.The structure theorem of solvable-semisimple groups: A group G is solv-able-semisimple if and only if G is the subdireet product of some prime groups.
Publication Year: 1985
Publication Date: 1985-01-01
Language: en
Type: article
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