On c-capability and n-isoclinic families of a specific class of groups

Let χ denote the class of all groups G such that Φ ( G ) ∩ Z ( G ) = 1 . In this paper, it is shown that the converse of Baer’s theorem holds for the groups in χ . Then we prove that the existence of the isomorphism between the center factors of the groups in χ suffices for those groups to be isocli...

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Bibliographic Details
Published in:Proceedings of the Indian Academy of Sciences. Mathematical sciences 2019-09, Vol.129 (4), p.1-9
Main Authors: Chakaneh, Marzieh, Kaheni, Azam, Kayvanfar, Saeed
Format: Article
Language:English
Subjects:
Isomorphism
Mathematics
Mathematics and Statistics
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Summary:Let χ denote the class of all groups G such that Φ ( G ) ∩ Z ( G ) = 1 . In this paper, it is shown that the converse of Baer’s theorem holds for the groups in χ . Then we prove that the existence of the isomorphism between the center factors of the groups in χ suffices for those groups to be isoclinic. We also prove that the isoclinism coincides with the n -isoclinism in χ . Finally, we obtain a criterion for c -capability of finite groups in χ .
ISSN:0253-4142
0973-7685
DOI:10.1007/s12044-019-0484-x