@article {
author = {Vaughan-Lee, M.},
title = {Understanding Wall's theorem on dependence of Lie relators in Burnside groups},
journal = {Journal of the Iranian Mathematical Society},
volume = {1},
number = {2},
pages = {129-143},
year = {2020},
publisher = {Iranian Mathematical Society},
issn = {2717-1612},
eissn = {2717-1612},
doi = {10.30504/jims.2020.107524},
abstract = {G.E. Wall [J. Algebra 104 (1986), no. 1, 1--22; Lecture Notes in Mathematics, pp. 191--197, 1456, Springer-Verlag, Berlin, 1990] gave two different proofs of a remarkable result about the multilinear Lie relators satisfied by groups of prime power exponent $q$. He showed that if $q$ is a power of the prime $p$, and if $f$ is a multilinear Lie relator in $n$ variables where $n\neq1\operatorname{mod}(p-1)$, then $f=0$ is a consequence of multilinear Lie relators in fewer than $n$ variables. For years I have struggled to understand his proofs, and while I still have not the slightest clue about his proof in [J. Algebra 104 (1986), no. 1, 1--22], I finally have some understanding of his proof in [Lecture Notes in Mathematics, pp. 91--197, 1456, Springer-Verlag, Berlin, 1990]. In this note I offer my insights into Wall's second proof of this theorem.},
keywords = {Lie relators,Burnside groups,Wall's theorem},
url = {http://jims.ims.ir/article_107524.html},
eprint = {http://jims.ims.ir/article_107524_f75dbbf7321a14000589885d5d7b9665.pdf}
}
@article {
author = {Pourmahmood-Aghababa, H. and Sattari, M. H.},
title = {Approximate biprojectivity and biflatness of some algebras over certain semigroups},
journal = {Journal of the Iranian Mathematical Society},
volume = {1},
number = {2},
pages = {145-155},
year = {2020},
publisher = {Iranian Mathematical Society},
issn = {2717-1612},
eissn = {2717-1612},
doi = {10.30504/jims.2020.107698},
abstract = {We investigate (bounded) approximate biprojectivity of $l^1(S)$ for uniformly locally finite inverse semigroups. As a consequence, we show that when $S=\mathcal{M}(G, I)$ is the Brandt inverse semigroup, then $l^1(S)$ is (boundedly) approximately biprojective if and only if $G$ is amenable. Moreover, we study biflatness and (bounded) approximate biprojectivity of the measure algebra $M(S)$ of a topological Brandt semigroup.},
keywords = {Banach algebras,approximate biprojectivity,biflatness,inverse semigroups},
url = {http://jims.ims.ir/article_107698.html},
eprint = {http://jims.ims.ir/article_107698_f1cce5a41ba06bdadbd87490a3330180.pdf}
}
@article {
author = {Bergman, G. M.},
title = {A note on factorizations of finite groups},
journal = {Journal of the Iranian Mathematical Society},
volume = {1},
number = {2},
pages = {157-161},
year = {2020},
publisher = {Iranian Mathematical Society},
issn = {2717-1612},
eissn = {2717-1612},
doi = {10.30504/jims.2020.108338},
abstract = {In Question 19.35 of the Kourovka Notebook, M. H. Hooshmand asks whether, given a finite group $G$ and a factorization $\mathrm{card}(G)= n_1\ldots n_k,$ one can always find subsets $A_1,\ldots,A_k$ of $G$ with $\mathrm{card}(A_i)=n_i$ such that $G=A_1\ldots A_k;$ equivalently, such that the group multiplication map $A_1\times\ldots\times A_k\to G$ is a bijection. We show that for $G$ the alternating goup on $4$ elements, $k=3,$ and $(n_1,n_2,n_3) = (2,3,2),$ the answer is negative. We then generalize some of the tools used in our proof, and note a related open question.},
keywords = {Factorization of a finite group,Product of subsets},
url = {http://jims.ims.ir/article_108338.html},
eprint = {http://jims.ims.ir/article_108338_8df75833b842c30981a08daf42636a75.pdf}
}
@article {
author = {Chimni, S. and Chinta, G. and Takloo-Bighash, R.},
title = {Counting subrings of $\mathbb{Z}^n$ of non-zero co-rank},
journal = {Journal of the Iranian Mathematical Society},
volume = {1},
number = {2},
pages = {163-172},
year = {2020},
publisher = {Iranian Mathematical Society},
issn = {2717-1612},
eissn = {2717-1612},
doi = {10.30504/jims.2020.238412.1020},
abstract = {In this paper we study subrings of $\mathbb{Z^{n+k}}$ of co-rank $k$. We relate the number of such subrings $R$ with torsion subgroup $(\mathbb{Z^{n+k}}/R)_{\rm{tor}}$ of size $r$ to the number of full rank subrings of $\mathbb{Z^n}$ of index $r$.},
keywords = {$mathbb{Z^n}$,subrings,Stirling numbers of the second kind},
url = {http://jims.ims.ir/article_118868.html},
eprint = {http://jims.ims.ir/article_118868_57f0145a78e287eccee85f1c2bbf2a9d.pdf}
}