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Proceedings of the American Mathematical Society

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A characterization of groups with isomorphic subgroups


Author: Donald W. Miller
Journal: Proc. Amer. Math. Soc. 33 (1972), 43-45
MSC: Primary 20F15
DOI: https://doi.org/10.1090/S0002-9939-1972-0292930-1
MathSciNet review: 0292930
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Abstract: The concept of normalizer is generalized to derive a characterization of groups G which contain a proper subgroup isomorphic to G.


References [Enhancements On Off] (What's this?)

  • [1] R. Baer, Groups without proper isomorphic quotient groups, Bull. Amer. Math. Soc. 50 (1944), 267-278. MR 5, 228. MR 0009955 (5:228a)
  • [2] R. A. Beaumont, Groups with isomorphic proper subgroups, Bull. Amer. Math. Soc. 51 (1945), 381-387. MR 7, 5. MR 0012294 (7:5i)
  • [3] J. R. Clay, The punctured plane is isomorphic to the unit circle, J. Number Theory 1 (1969), 500-501. MR 40 #227. MR 0246958 (40:227)
  • [4] I. Kaplansky, A note on groups without isomorphic subgroups, Bull. Amer. Math. Soc. 51 (1945), 529-530. MR 7. 2. MR 0012267 (7:2b)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0292930-1
Keywords: Isomorphic subgroup, normalizer, holomorph
Article copyright: © Copyright 1972 American Mathematical Society

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