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Characterization of Finite Groups by the Number of Non-cyclic Non-TI-subgroups

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Abstract

Let G be a finite group and M a subgroup of G. Then M is said to be a TI-subgroup of G if \(M^g\cap M=1\) or M for any \(g\in G\). In this paper, we characterize the solvability of finite groups only by the number of their non-cyclic non-TI-subgroups, we prove that any finite group G having at most 26 non-cyclic non-TI-subgroups is always solvable except for \(G\cong A_5\) or \(\hbox {SL}(2,5)\).

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Acknowledgments

The authors are grateful to all referees who give valuable comments and suggestions.

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Correspondence to Jiangtao Shi.

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Communicated by V. Ravichandran.

Jiangtao Shi was supported by NSFC (Grant 11201401). Cui Zhang was supported by NSFC (Grant 11201403).

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Shi, J., Zhang, C. Characterization of Finite Groups by the Number of Non-cyclic Non-TI-subgroups. Bull. Malays. Math. Sci. Soc. 39, 1457–1463 (2016). https://doi.org/10.1007/s40840-015-0247-5

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  • DOI: https://doi.org/10.1007/s40840-015-0247-5

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