شماره ركورد كنفرانس :
4371
عنوان مقاله :
Generalized exponent of groups
پديدآورندگان :
Abdollahi .A a.abdollahi@math.ui.ac.ir University of Isfahan , Daoud .B boun_daoud@yahoo.fr Ferhat Abbas University , Farrokhi D. G .M m.farrokhi.d.g@gmail.com Muroran Institute of Technology , Guerboussa .Y yassine_guer@hotmail.fr University Kasdi Merbah Ouargla
كليدواژه :
Generalized exponent , polynomial identity
عنوان كنفرانس :
دهمين كنفرانس ملي نظريه گروه هاي ايران
چكيده فارسي :
A group $G$ satisfies a positive generalized identity of degree $n$ if there exist elements $g_1,\ldots,g_n\in G$ such that $x^{g_1}\cdots x^{g_n}=1$ for all $x\in G$. The minimum degree of such an identity is called the generalized exponent of $G$. Among other things, we prove that every finitely generated solvable group satisfying a positive generalized identity of prime degree is a finite $p$-group. Consequently, we show that every finite group with a positive generalized identity of degree $5$ is a $5$-group of exponent dividing $25$
