NON-ABELIAN TENSOR ABSOLUTE CENTRE OF A GROUP

Authors

  • Mohammad Reza Hassanlee Islamic Azad University, Mashhad Branch
  • Mohammad Reza Rajabzadeh Moghaddam Khayyam University and Ferdowsi University of Mashhad
  • Mohammad Amin Rostamyari Khayyam University

Keywords:

Non-abelian tensor product, auto-Engel element, autocommutator subgroup, absolute centre.

Abstract

Abstract. In 1904, Schur proved his famous result which says that if the central factor group of a given group is finite then so is its derived subgroup. In 1994, Hegarty showed that if the absolute central factor group, G/L(G), is finite then so is its autocommutator subgroup, K(G).

Using the notion of non-abelian tensor product, we introduce the concept of tensor absolute centre, ‎$L^\otimes (G)$, and $K^\otimes(G)=G\otimes {\rm Aut}(G)$. Then under some condition we prove that the finiteness of $G/L^\otimes(G)$ implies that $K^\otimes(G)$ is also finite.

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Published

2019-03-13

Issue

Vol. 13

Section

Vol. 13, No. 3, (2019)

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