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On verifying lattice isomorphisms between groups. (English) Zbl 0545.20017

The author proves that any isomorphism between the posets of two- generator subgroups of a pair of groups lifts to a unique isomorphism between the full lattices of all their subgroups.

MSC:

20E15 Chains and lattices of subgroups, subnormal subgroups
Full Text: DOI

References:

[1] A. W. Jones, The lattice isomorphisms of certain finite groups. Duke Math. J.12, 541-560 (1945). · Zbl 0063.03062 · doi:10.1215/S0012-7094-45-01249-X
[2] K. Iwasawa, On the structure of infiniteM-groups. Japan. J. Math.18, 709-728 (1943). · Zbl 0061.02504
[3] O. Ore, Structures and group theory II. Duke Math. J.4, 247-269 (1938). · JFM 64.0055.01 · doi:10.1215/S0012-7094-38-00419-3
[4] S. Sato, Note on lattice-isomorphisms between abelian groups and non-abelian groups. Osaka J. Math.3, 215-220 (1951). · Zbl 0044.01104
[5] M.Suzuki, Structure of a group and the structure of its lattice of subgroups. Berlin 1956. · Zbl 0070.25406
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