journal6 ›› 2003, Vol. 24 ›› Issue (2): 23-25.
• Doctoral Forum • Previous Articles Next Articles
Online:
Published:
Abstract: Based on the concept of (∈,∈∨q)-fuzzy subgroup introduced by S.K.Bhakat in 1992,the notions of (∈,∈∨q)- fuzzy normalizer and (∈,∈∨q)-fuzzy centralizer are introduced.Some properties of (∈,∈∨q)-fuzzy normalizer and (∈,∈∨q)- fuzzy centralizer are discussed.Then,the definition of(∈,∈∨q)- fuzzy quotient group and (∈,∈∨q)-fuzzy quotient subgroup is given.At last,the isomorphism theorem for (∈,∈∨q)-fuzzy quotient group is established.The main results include:(1)if is a fuzzy subset of,then the (∈,∈∨q)-fuzzy normalizer of is a subgroup of;(2)if is a fuzzy subgroup of,then the (∈,∈∨q)-fuzzy centralizer of is a subgroup of and a normal subgroup of;(3)if and are (∈,∈∨q)-fuzzy normal subgroup and (∈,∈∨q)-fuzzy subgroup of,respectively,then is a (∈,∈∨q)-fuzzy subgroup of.
Key words: (∈, ∈∨q)-fuzzy subgroup;(∈, ∈∨q)-fuzzy normal subgroup;(∈, ∈∨q)-fuzzy normalizer;(∈, ∈∨q)-fuzzy centralizer;(∈, ∈∨q)-fuzzy quotient subgroup
YAO Bing-Xue. (∈,∈∨q)-Fuzzy Normalizer and (∈,∈∨q)-Fuzzy Quotient Subgroup[J]. journal6, 2003, 24(2): 23-25.
Add to citation manager EndNote|Ris|BibTeX
URL: https://zkxb.jsu.edu.cn/EN/
https://zkxb.jsu.edu.cn/EN/Y2003/V24/I2/23