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Research articles

ScienceAsia 43(2017): 319-325 |doi: 10.2306/scienceasia1513-1874.2017.43.319

Commutator subgroups of Vershik-Kerov groups for infinite symplectic groups

Xin Hou*, Shangzhi Li, Yucheng Yang

ABSTRACT:     Let R be a commutative ring with identity 1. We describe two kinds of Vershik-Kerov groups for the symplectic case: SpVK(2,∞,R) and GSpVK(2,∞,R). We also determine the commutator subgroups of these groups over a wide class of commutative rings. For an arbitrary infinite field, we find the bounds for the commutator width of the groups SpVK(2,∞,K) and GSpVK(2,∞,K).

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LMIB and School of Mathematics and Systems Science, Beihang University, Beijing, 100191, China

* Corresponding author, E-mail: houge19870512@126.com

Received 9 Jun 2017, Accepted 28 Oct 2017