Fully transitive <IMG >-groups with finite first Ulm subgroup期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Fully transitive -groups with finite first Ulm subgroup

Authors:	Agnes T. Paras Lutz Strü ngmann

Affiliation:	Department of Mathematics, University of the Philippines at Diliman, 1101 Quezon City, Philippines ; Fachbereich 6, Mathematik, University of Essen, 45117 Essen, Germany

Abstract:	An abelian -group is called (fully) transitive if for all with ( ) there exists an automorphism (endomorphism) of which maps onto . It is a long-standing problem of A. L. S. Corner whether there exist non-transitive but fully transitive -groups with finite first Ulm subgroup. In this paper we restrict ourselves to -groups of type , this is to say -groups satisfying $mathrm{Aut}(G)upharpoonright_{ p^{omega}G} = U(mathrm{End}(G) upharpoonright_{p^{omega}G})$ . We show that the answer to Corner's question is no if $p^{omega}G$ is finite and is of type .

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