A characterization of groups with isomorphic subgroups
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- by Donald W. Miller
- Proc. Amer. Math. Soc. 33 (1972), 43-45
- DOI: https://doi.org/10.1090/S0002-9939-1972-0292930-1
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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
- Reinhold Baer, Groups without proper isomorphic quotient groups, Bull. Amer. Math. Soc. 50 (1944), 267–278. MR 9955, DOI 10.1090/S0002-9904-1944-08134-2
- Ross A. Beaumont, Groups with isomorphic proper subgroups, Bull. Amer. Math. Soc. 51 (1945), 381–387. MR 12294, DOI 10.1090/S0002-9904-1945-08359-1
- James R. Clay, The punctured plane is isomorphic to the unit circle, J. Number Theory 1 (1969), 500–501. MR 246958, DOI 10.1016/0022-314X(69)90011-0
- Irving Kaplansky, A note on groups without isomorphic subgroups, Bull. Amer. Math. Soc. 51 (1945), 529–530. MR 12267, DOI 10.1090/S0002-9904-1945-08382-7
Bibliographic Information
- © Copyright 1972 American Mathematical Society
- 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