156,517 research outputs found
Personal Papers (MS 80-0002)
No full textLetter from David Cohen to I. H. Kempner discussing the loan Kempner provided to Cohen's grandson and requesting a loan for the Houston Hat Company to get merchandise
Personal Papers (MS 80-0002)
No full textLetter from I. H. Kempner to Henry Cohen discussing the Kempner family's recent charitable gifts
Personal Papers (MS 80-0002)
No full textLetter from David Cohen to I. H. Kempner discussing the financial assistance Kempner provided him
Personal Papers (MS 80-0002)
No full textLetter from Henry Cohen to I. H. Kempner discussing the recent charitable gifts of the Kempner family
Personal Papers (MS 80-0002)
No full textLetter from Herman Cohen to I. H. Kempner thanking Kempner for the check he sent and discussing his current health situation
Personal Papers (MS 80-0002)
No full textLetter from Herman Cohen to I. H. Kempner discussing Cohen's recovery from his operation and thanking Kempner for the help with his medical expenses
Personal Papers (MS 80-0002)
No full textLetter from Herman Cohen to I. H. Kempner discussing Kempner's generosity with providing financial assistance and requesting help with another medical bill
Personal Papers (MS 80-0002)
No full textLetter from Herman Cohen to I. H. Kempner thanking Kempner for the check he sent and updating him on his recovery progress
Personal Papers (MS 80-0002)
No full textLetter from Herman Cohen to I. H. Kempner thanking Kempner for the check covering Cohen's medical bill from Dr. Harold D. Buttery and discussing the circumstances of the bill
On the local-indicability cohen–lyndon theorem
No full textFor a group H and a subset X of H, we let HX denote the set {hxh?1 | h ? H, x ? X}, and when X is a free-generating set of H, we say that the set HX is a Whitehead subset of H. For a group F and an element r of F, we say that r is Cohen–Lyndon aspherical in F if F{r} is a Whitehead subset of the subgroup of F that is generated by F{r}. In 1963, Cohen and Lyndon (D. E. Cohen and R. C. Lyndon, Free bases for normal subgroups of free groups, Trans. Amer. Math. Soc. 108 (1963), 526–537) independently showed that in each free group each non-trivial element is Cohen–Lyndon aspherical. Their proof used the celebrated induction method devised by Magnus in 1930 to study one-relator groups. In 1987, Edjvet and Howie (M. Edjvet and J. Howie, A Cohen–Lyndon theorem for free products of locally indicable groups, J. Pure Appl. Algebra 45 (1987), 41–44) showed that if A and B are locally indicable groups, then each cyclically reduced element of A*B that does not lie in A ? B is Cohen–Lyndon aspherical in A*B. Their proof used the original Cohen–Lyndon theorem. Using Bass–Serre theory, the original Cohen–Lyndon theorem and the Edjvet–Howie theorem, one can deduce the local-indicability Cohen–Lyndon theorem: if F is a locally indicable group and T is an F-tree with trivial edge stabilisers, then each element of F that fixes no vertex of T is Cohen–Lyndon aspherical in F. Conversely, by Bass–Serre theory, the original Cohen–Lyndon theorem and the Edjvet–Howie theorem are immediate consequences of the local-indicability Cohen–Lyndon theorem. In this paper we give a detailed review of a Bass–Serre theoretical form of Howie induction and arrange the arguments of Edjvet and Howie into a Howie-inductive proof of the local-indicability Cohen–Lyndon theorem that uses neither Magnus induction nor the original Cohen–Lyndon theorem. We conclude with a review of some standard applications of Cohen–Lyndon asphericit
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