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1. Bounding conjugacy depth functions for wreath products of finitely generated abelian groups

   https://doi.org/10.46298/jgcc.2023.15.1.11728  

   Ferov, Michal; Pengitore, Mark (September 2023, journal of Groups, complexity, cryptology)

   In this article, we study the asymptotic behaviour of conjugacy separabilityfor wreath products of abelian groups. We fully characterise the asymptoticclass in the case of lamplighter groups and give exponential upper and lowerbounds for generalised lamplighter groups. In the case where the base group isinfinite, we give superexponential lower and upper bounds. We apply our resultsto obtain lower bounds for conjugacy depth functions of various wreath productsof groups where the acting group is not abelian. 

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2. Finite image homomorphisms of the braid group and its generalizations

   https://doi.org/10.1017/S0017089523000022  

   Scherich, Nancy; Verberne, Yvon (March 2023, Glasgow Mathematical Journal)

   Abstract. Using totally symmetric sets, Chudnovsky–Kordek–Li–Partin gave a superexponential lower bound on the cardinality of non-abelian finite quotients of the braid group. In this paper, we develop new techniques using multiple totally symmetric sets to count elements in non-abelian finite quotients of the braid group. Using these techniques, we improve the lower bound found by Chudnovsky et al. We exhibit totally symmetric sets in the virtual and welded braid groups and use our new techniques to find superexponential bounds for the finite quotients of the virtual and welded braid groups. 

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3. Are stay-at-home orders more difficult to follow for low-income groups?

   https://doi.org/10.1016/j.jtrangeo.2020.102894  

   Lou, Jiehong; Shen, Xingchi; Niemeier, Deb (December 2020, Journal of transport geography)

   In response to the COVID-19 pandemic, a growing number of states, counties and cities in the United States issued mandatory stay-at-home orders as part of their efforts to slow down the spread of the virus. We argue that the consequences of this one-size-fits-all order will be differentially distributed among economic groups. In this paper, we examine social distance behavior changes for lower income populations. We conduct a comparative analysis of responses between lower-income and upper-income groups and assess their relative exposure to COVID-19 risks. Using a difference-in-difference-in-differences analysis of 3140 counties, we find social distance policy effect on the lower-income group is smaller than that of the upper-income group, by as much as 46% to 54%. Our explorations of the mechanisms behind the disparate effects suggest that for the work-related trips the stay-at-home orders do not significantly reduce low income work trips and this result is statistically significant. That is, the share of essential business defined by stay-at-home orders is significantly negatively correlated with income at county level. In the non-work-related trips, we find that both the lower-income and upper-income groups reduced visits to retail, recreation, grocery, and pharmacy visits after the stay-at-home order, with the upper-income group reducing trips more compared to lower-income group. 

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4. Assigned group work is associated with increased student motivation and perceptions of belonging in an asynchronous online physiology laboratory course

   https://doi.org/10.1152/advan.00064.2024  

   Carr, Shea E; Wilson, Thad E; Slone, Stacey A; Karanja, Leila W; Osterhage, Jennifer L (September 2024, Advances in Physiology Education)

   This study explores the effect of assigned group work in an asynchronous online physiology laboratory course on student motivation and belonging. Students’ perceptions of belonging and competence-related beliefs were higher, and effort and psychological costs were lower, when assigned to groups compared to students not assigned to groups. Students assigned to groups noted peer interactions as the most inclusive aspect of the course, whereas instructor interactions were noted as inclusive by those not assigned group work. 

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5. Rank of Matrices with Entries from a Multiplicative Group

   https://doi.org/10.1093/imrn/rnac183  

   Alon, Noga; Solymosi, József (July 2022, International Mathematics Research Notices)

   Abstract We establish lower bounds on the rank of matrices in which all but the diagonal entries lie in a multiplicative group of small rank. Applying these bounds we show that the distance sets of finite pointsets in $$\mathbb {R}^d$$ generate high-rank multiplicative groups and that multiplicative groups of small rank cannot contain large sumsets. 

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