Glasnik Matematicki, Vol. 49, No. 1 (2014), 105-111.

FINITE GROUPS HAVING AT MOST 27 NON-NORMAL PROPER SUBGROUPS OF NON-PRIME-POWER ORDER

Jiangtao Shi and Cui Zhang

School of Mathematics and Information Science, Yantai University, Yantai 264005, China
e-mail: jiangtaoshi@126.com

Department of Applied Mathematics and Computer Science, Technical University of Denmark, DK-2800 Lyngby, Denmark
e-mail: cuizhang2008@gmail.com


Abstract.   We prove that any finite group having at most 27 non-normal proper subgroups of non-prime-power order is solvable except for G≅ A5, the alternating group of degree 5.

2010 Mathematics Subject Classification.   20D10.

Key words and phrases.   Finite group, solvable group, subgroup of non-prime-power order.


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DOI: 10.3336/gm.49.1.08


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