| Title: |
A NOTE ON NON-SOLVABLE GROUPS WITH GIVEN NUMBER OF PARTICULAR SUBGROUPS. |
| Authors: |
Jiangtao SHI, Fanjie XU, Yifan LIU |
| Source: |
Proceedings of the Romanian Academy, Series A: Mathematics, Physics, Technical Sciences, Information Science; Oct-Dec2024, Vol. 25 Issue 4, p287-291, 5p |
| Subject Terms: |
FINITE groups, GROUP theory, NILPOTENT groups, FEIT-Thompson theorem, CONJUGACY classes |
| Abstract: |
Considering the quantitative properties of some particular subgroups of a finite group, we prove that (1) a non-solvable group G has exactly 5 non-subnormal non-supersolvable proper subgroups if and only if G∼= A5 or SL2(5). (2) a non-solvable group G has exactly 5 non-subnormal non-2-nilpotent proper subgroups if and only if G∼= A5 or SL2(5). (3) a non-solvable group G has exactly 16 non-subnormal non-2-closed proper subgroups (or two same order classes of non-subnormal non-2-closed proper subgroups) if and only if G∼= A5 or SL2(5). Our results improve some known related research. [ABSTRACT FROM AUTHOR] |
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| Database: |
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