ScienceAsia 43 (2017): 319-325 |doi:
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: email@example.com
Received 9 Jun 2017, Accepted 28 Oct 2017