Rank and abelian rank of systems of equations over the free group
نویسندگان
چکیده
منابع مشابه
Fuzzy Subgroups of Rank Two Abelian p-Group
In this paper we enumerate fuzzy subgroups, up to a natural equivalence, of some finite abelian p-groups of rank two where p is any prime number. After obtaining the number of maximal chains of subgroups, we count fuzzy subgroups using inductive arguments. The number of such fuzzy subgroups forms a polynomial in p with pleasing combinatorial coefficients. By exploiting the order, we label the s...
متن کاملfuzzy subgroups of rank two abelian p-group
in this paper we enumerate fuzzy subgroups, up to a natural equivalence, of some finite abelian p-groups of rank two where p is any prime number. after obtaining the number of maximal chains of subgroups, we count fuzzy subgroups using inductive arguments. the number of such fuzzy subgroups forms a polynomial in p with pleasing combinatorial coefficients. by exploiting the order, we label the s...
متن کاملSome quadratic equations in the free group of rank 2
For a given quadratic equation with any number of unknowns in any free group F , with right-hand side an arbitrary element of F , an algorithm for solving the problem of the existence of a solution was given by Culler [8] using a surface method and generalizing a result of Wicks [46]. Based on different techniques, the problem has been studied by the authors [11; 12] for parametric families of ...
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Ngcibi, Murali and Makamba [Fuzzy subgroups of rank two abelian$p$-group, Iranian J. of Fuzzy Systems {bf 7} (2010), 149-153]considered the number of fuzzy subgroups of a finite abelian$p$-group $mathbb{Z}_{p^m}times mathbb{Z}_{p^n}$ of rank two, andgave explicit formulas for the cases when $m$ is any positiveinteger and $n=1,2,3$. Even though their method can be used for thecases when $n=4,5,l...
متن کاملCOUNTING DISTINCT FUZZY SUBGROUPS OF SOME RANK-3 ABELIAN GROUPS
In this paper we classify fuzzy subgroups of a rank-3 abelian group $G = mathbb{Z}_{p^n} + mathbb{Z}_p + mathbb{Z}_p$ for any fixed prime $p$ and any positive integer $n$, using a natural equivalence relation given in cite{mur:01}. We present and prove explicit polynomial formulae for the number of (i) subgroups, (ii) maximal chains of subgroups, (iii) distinct fuzzy subgroups, (iv) non-isomorp...
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ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 1998
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s001309150001960x