On a Problem of P. Hall about Groups Isomorphic to all their Non-Trivial Normal Subgroups |
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Authors: | Obraztsov Viatcheslav N |
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Institution: | Department of Mathematics, University of Melbourne Parkville, Victoria 3052, Australia |
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Abstract: | A scheme of construction of infinite groups, other than simplegroups, free groups of infinite rank and the infinite cyclicgroup, which are isomorphic to all their non-trivial normalsubgroups is presented. Some results about the automorphismgroups of simple infinite groups are also obtained. In particular,it is proved that there is an infinite group G of any sufficientlylarge prime exponent p (or which is torsion-free) all of whoseproper subgroups are cyclic, and such that the groups Aut Gand Out G are isomorphic. The proofs use the technique of gradeddiagrams developed by A. Yu. Ol'shanskii. 1991 Mathematics SubjectClassification: 20F05, 20F06. |
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Keywords: | normal subgroup automorphism group graded diagram |
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