The notion of exterior centralizer $C^\wedge_G(x)$ of an element $x$ of a group $G$ is introduced in the present paper in order to improve some known results on the nonabelian tensor product of two groups. We study the structure of $G$ by looking at that of $C^\wedge_G(x)$ and we find some bounds for the Schur multiplier $M(G)$ of $G$.
Niroomand, P., Russo, F. (2009). A note on the exterior centralizer. ARCHIV DER MATHEMATIK, 93, 505-512 [10.1007/s00013-009-0077-5].
A note on the exterior centralizer
RUSSO, Francesco
2009-01-01
Abstract
The notion of exterior centralizer $C^\wedge_G(x)$ of an element $x$ of a group $G$ is introduced in the present paper in order to improve some known results on the nonabelian tensor product of two groups. We study the structure of $G$ by looking at that of $C^\wedge_G(x)$ and we find some bounds for the Schur multiplier $M(G)$ of $G$.
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