Non-hyperbolic automatic groups and groups acting on CAT(0) cube complexes

• Nakagawa, Yoshiyuki

• Tamura, Makoto

• Yamashita, Yasushi

抄録

type:Article

Preprint of an article published in [Int. J. Algebra Comput. Vol.24, No.6(2014), pp.795-813 ] [http://dx.doi.org/10.1142/S0218196714500349] 〓 [copyright World Scientific Publishing Company] [http://www.worldscientific.com/worldscinet/ijac] Electronic version of an article published as [Int. J. Algebra Comput. Vol.24, No.6(2014), pp.795-813] [http://dx.doi.org/10.1142/S0218196714500349] 〓 [copyright World Scientific Publishing Company] [http://www.worldscientific.com/worldscinet/ijac]

We discuss a problem posed by Gersten: Is every automatic group which does not contain Ζ × Ζ subgroup, hyperbolic? To study this question, we define the notion of "n-track of length n", which is a structure like Ζ × Ζ, and prove its existence in the non-hyperbolic automatic groups with mild conditions. As an application, we show that if a group acts freely, cellularly, properly discontinuously and cocompactly on a CAT(0) cube complex and its quotient is "weakly special", then the above question is answered affirmatively.

収録刊行物

• International Journal of Algebra and Computation

  International Journal of Algebra and Computation 24 (6), 795-813, 2014-09-03

  World Scientific Publishing

キーワード

• Automatic group
• hyperbolic group
• CAT(0) cube complex

詳細情報

• CRID: 1050845763322080256
• NII論文ID: 120006658111
• NII書誌ID: AA10875347
• ISSN: 02181967
• ISSN: 17936500
• DOI: 10.1142/s0218196714500349
• Web Site: http://hdl.handle.net/10935/4371
• Web Site: https://www.worldscientific.com/doi/pdf/10.1142/S0218196714500349
• 本文言語コード: en
• 資料種別: journal article
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