Solvable $L$-subgroup of an $L$-group

Document Type: Research Paper


1 Department of Mathematics, Ramjas College,, University of Delhi,, Delhi-110007, India

2 Department of Mathematics, Zakir Husain Delhi College,, J.N.Marg, University of Delhi, Delhi-110006, India


In this paper, we study the notion of solvable $L$-subgroup of an $L$-group and provide its level subset characterization and this justifies the suitability of this extension. Throughout this work, we have used normality of an $L$-subgroup of an $L$-group in the sense of Wu rather than Liu.


[1] N. Ajmal, Fuzzy groups with sup property, Inform. Sci., 93 (1996), 247-264.
[2] N. Ajmal and I. Jahan , A study of normal fuzzy subgroups and characteristic fuzzy subgroups
of a fuzzy group, Fuzzy Information and Engineering, 2 (2012), 123-143.
[3] N. Ajmal and I. Jahan, Nilpotency and theory of L-subgroups of an L-group, Fuzzy Informa-
tion and Engineering, 6 (2014), 1-17.
[4] N. Ajmal and A. Jain, Some constructions of the join of fuzzy subgroups and certain lattices
of fuzzy subgroups with sup property, Inform. Sci., 179 (2009), 4070-4082.
[5] N. Ajmal and I. Jahan,Generated L-subgroup of an L-group, Iranian Journal of Fuzzy Sys-
tems, 12(2) (2015), 129-136.
[6] J. A. Goguen, Lfuzzy sets, J. Math. Anal. Appl., 18 (1967), 145-174.
[7] K. C. Gupta and B. K. Sarma, nilpotent fuzzy groups, Fuzzy Sets and Systems, 101 (1999),
[8] W. J. Liu, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets and Systems, 8 (1982),
[9] D. S. Malik, J. N. Mordeson and P. S. Nair, Fuzzy normal subgroups in fuzzy subgroups, J.
Korean Math. Soc., 29 (1992), 1-8.
[10] L. Martinez, L Fuzzy subgroups of fuzzy groups and fuzzy ideals of fuzzy rings, J. Fuzzy
Math., 3 (1995), 833-849.
[11] J. N. Mordeson, K. R. Bhutani and A. Rosenfeld, Fuzzy group theory, Springer, 2005.
[12] J. N. Mordeson and D. S. Malik, Fuzzy commutative algebra, World Scienti c, 1998.
[13] N. P. Mukherjee and P. Bhattacharya, Fuzzy groups: some group-theoretic analogs, Inform.
Science, 39 (1986), 247-268.
[14] A. S. Prajapati and N. Ajmal, Maximal ideals of L-subrings, J. Fuzzy Math., 15 (1999),
[15] A. S. Prajapati and N. Ajmal,Maximal ideals of L{subrings. II, J. Fuzzy Math., 15 (2007),
[16] M. G. Ranitovic and A. Tepavcevic, General form of lattice-valued fuzzy sets under the
cutworthy approach, Fuzzy Sets and Systems, 158 (2007), 1213-1216.
[17] S. Ray, Solvable fuzzy groups, Inform. Science 75 (1993) 47-61.
[18] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35 (1971), 512-517.
[19] B. K. Sarma, Solvable fuzzy groups, Fuzzy Sets and Systems, 106 (1999), 463-467.
[20] B. Seselja, D. Stojic and A. Tepavcevic, On existence of P-valued fuzzy sets with a given
collection of cuts, Fuzzy Sets and Systems, 161 (2010), 763-768.
[21] B. Seselja and A. Tepavcevic,Completion of ordered structures by cuts of fuzzy sets: an
overview, Fuzzy Sets and Systems, 136 (2003), 1-19.
[22] W. Wu, Normal fuzzy subgroups, Fuzzy Math., 1 (1981), 21-30.