Failure of the finitely generated intersection property for ascending HNN extensions of free groups

Jacob Bamberger; Daniel T. Wise

doi:10.1142/S0218196722500370

Failure of the finitely generated intersection property for ascending HNN extensions of free groups

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Abstract

The main result in this paper is the failure of the finitely generated intersection property (FGIP) of ascending HNN extensions of non-cyclic finite rank free groups. This class of groups consists of free-by-cyclic groups and properly ascending HNN extensions of free groups. We also give a sufficient condition for the failure of the FGIP in the context of relative hyperbolicity, we apply this to free-by-cyclic groups of exponential growth.

Original language	English
Pages (from-to)	885-893
Number of pages	9
Journal	International Journal of Algebra and Computation
Volume	32
Issue number	5
DOIs	https://doi.org/10.1142/S0218196722500370
State	Published - 1 Aug 2022
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1142/S0218196722500370

Cite this

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abstract = "The main result in this paper is the failure of the finitely generated intersection property (FGIP) of ascending HNN extensions of non-cyclic finite rank free groups. This class of groups consists of free-by-cyclic groups and properly ascending HNN extensions of free groups. We also give a sufficient condition for the failure of the FGIP in the context of relative hyperbolicity, we apply this to free-by-cyclic groups of exponential growth.",

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AU - Wise, Daniel T.

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Y1 - 2022/8/1

N2 - The main result in this paper is the failure of the finitely generated intersection property (FGIP) of ascending HNN extensions of non-cyclic finite rank free groups. This class of groups consists of free-by-cyclic groups and properly ascending HNN extensions of free groups. We also give a sufficient condition for the failure of the FGIP in the context of relative hyperbolicity, we apply this to free-by-cyclic groups of exponential growth.

AB - The main result in this paper is the failure of the finitely generated intersection property (FGIP) of ascending HNN extensions of non-cyclic finite rank free groups. This class of groups consists of free-by-cyclic groups and properly ascending HNN extensions of free groups. We also give a sufficient condition for the failure of the FGIP in the context of relative hyperbolicity, we apply this to free-by-cyclic groups of exponential growth.

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U2 - 10.1142/S0218196722500370

DO - 10.1142/S0218196722500370

M3 - مقالة

SN - 0218-1967

VL - 32

SP - 885

EP - 893

JO - International Journal of Algebra and Computation

JF - International Journal of Algebra and Computation

IS - 5

ER -

Failure of the finitely generated intersection property for ascending HNN extensions of free groups

Abstract

All Science Journal Classification (ASJC) codes

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