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| Finite Non-abelian Groups Whose Non-abelianSubgroups Have Minimum Centralizers |
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Citation： |
Dandan ZHANG,Haipeng QU,Yanfeng LUO.Finite Non-abelian Groups Whose Non-abelianSubgroups Have Minimum Centralizers[J].Chinese Annals of Mathematics B,2026,(3):529~554 |
| Page view： 89
Net amount： 43 |
Authors： |
Dandan ZHANG; Haipeng QU;Yanfeng LUO |
Foundation： |
the National Natural Science Foundation of China (Nos. 12571018,
12171213, 11771258). |
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| Abstract： |
A finite non-abelian group G is called an MC-group if all non-abelian subgroups
H of G have minimum centralizers (i.e., CG(H) = Z(G)). In this paper, the authors give
some characterizations of MC-groups, and it is proved that MC-groups are just the finite
groups with modular centralizer lattice of length 2 depicted by Schmidt, which leads to a
classification of MC-groups. However, Schmidt’s depiction said nothing for MC-p-groups.
They give a characterization of MC-p-groups. In particular, they characterize special
MC-p-groups by means of the commutator matrices, and provide a method to determine
or classify special MC-p-groups. As applications, some examples are given, and special
MC-p-groups with an abelian maximal subgroup are classified up to isoclinism. |
Keywords： |
Centralizers of groups Finite p-groups Special p-groups Isoclinism,
Commutator matrix |
Classification： |
20D15, 20D30, 05C25 |
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