Densities for Ranks of Certain Parts of p-Class Groups

1987 ◽  
Vol 99 (1) ◽  
pp. 1 ◽  
Author(s):  
Frank Gerth III
Keyword(s):  
Class Groups

The Nielsen-Thurston Classification

2017 ◽  
Author(s):  
Benson Farb ◽  
Dan Margalit
Keyword(s):  
Hyperbolic Geometry ◽  
Mapping Class Groups ◽  
Classification Theorem ◽  
Mapping Class ◽  
Fundamental Result ◽  
Class Groups ◽  
Mapping Torus ◽  
Higher Genus ◽  
Manifold Theory

This chapter explains and proves the Nielsen–Thurston classification of elements of Mod(S), one of the central theorems in the study of mapping class groups. It first considers the classification of elements for the torus of Mod(T² before discussing higher-genus analogues for each of the three types of elements of Mod(T². It then states the Nielsen–Thurston classification theorem in various forms, as well as a connection to 3-manifold theory, along with Thurston's geometric classification of mapping torus. The rest of the chapter is devoted to Bers' proof of the Nielsen–Thurston classification. The collar lemma is highlighted as a new ingredient, as it is also a fundamental result in the hyperbolic geometry of surfaces.

Pointwise bound for ℓ-torsion in class groups: Elementary abelian extensions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Jiuya Wang
Keyword(s):  
Galois Group ◽  
Prime Number ◽  
Finite Groups ◽  
Upper Bound ◽  
Abelian Groups ◽  
Class Groups ◽  
Abelian Extensions ◽  
Pointwise Bound ◽  
First Case

AbstractElementary abelian groups are finite groups in the form of {A=(\mathbb{Z}/p\mathbb{Z})^{r}} for a prime number p. For every integer {\ell>1} and {r>1}, we prove a non-trivial upper bound on the {\ell}-torsion in class groups of every A-extension. Our results are pointwise and unconditional. This establishes the first case where for some Galois group G, the {\ell}-torsion in class groups are bounded non-trivially for every G-extension and every integer {\ell>1}. When r is large enough, the unconditional pointwise bound we obtain also breaks the previously best known bound shown by Ellenberg and Venkatesh under GRH.

Social Class and Code Elaboration in Oral Communication

1971 ◽  
Vol 14 (2) ◽  
pp. 421-427 ◽  
Author(s):  
Millicent E. Poole ◽  
T. W. Field
Keyword(s):  
Social Class ◽  
Middle Class ◽  
Working Class ◽  
Oral Communication ◽  
Class Groups ◽  
Parental Occupation ◽  
The Social ◽  
Linguistic Coding

The Bernstein thesis of elaborated and restricted coding orientation in oral communication was explored at an Australian tertiary institute. A working-class/middle-class dichotomy was established on the basis of parental occupation and education, and differences in overall coding orientation were found to be associated with social class. This study differed from others in the area in that the social class groups were contrasted in the totality of their coding orientation on the elaborated/restricted continuum, rather than on discrete indices of linguistic coding.

scholarly journals On invariance of the Euler class groups under a subintegral base change

2014 ◽  
Vol 398 ◽  
pp. 131-155 ◽  
Author(s):  
Mrinal Kanti Das ◽  
Md. Ali Zinna
Keyword(s):  
Euler Class ◽  
Base Change ◽  
Class Groups

On the Teichmüller tower of mapping class groups

2000 ◽  
Vol 2000 (521) ◽  
pp. 1-24 ◽  
Author(s):  
Allen Hatcher ◽  
Pierre Lochak ◽  
Leila Schneps
Keyword(s):  
Mapping Class Groups ◽  
Mapping Class ◽  
Class Groups

scholarly journals Black holes and class groups

2018 ◽  
Vol 5 (4) ◽  
Author(s):  
Nathan Benjamin ◽  
Shamit Kachru ◽  
Ken Ono ◽  
Larry Rolen
Keyword(s):  
Black Holes ◽  
Class Groups

Is Retirement a Crisis for Men? Class and Adjustment to Retirement

2017 ◽  
Vol 23 (2) ◽  
pp. 306-325 ◽  
Author(s):  
Ilkka Pietilä ◽  
Toni Calasanti ◽  
Hanna Ojala ◽  
Neal King
Keyword(s):  
Paid Work ◽  
Class Groups ◽  
Popular Discourse ◽  
Metal Workers ◽  
Retirement Expectations ◽  
Crisis Discourse ◽  
Crisis Of Masculinity ◽  
Using Data ◽  
Retirement Crisis

Because paid work is taken to be central to manhood, scholarly and popular discourse have characterized retirement as presenting a “crisis of masculinity.” However, such a crisis is not borne out by research, perhaps because scholars have not considered how class might shape masculinities and thus expectations and experiences of retirement. Using data obtained from interviews with Finnish metal workers and engineers who are either approaching retirement or recently retired, we ask whether (1) this crisis discourse is reflected in their retirement expectations, (2) it matches their actual experiences of retirement, and (3) retirement disrupts the masculinities of some class groups more than others. We find evidence of this retirement crisis discourse in our respondents’ views of retirement, but not in their actual experiences, belying the homogeneity of masculinity implied by it. Class shapes both the perceived content of crises and the actual retirement experiences.

scholarly journals Divisor class groups of affine semigroup rings associated with distributive lattices

1992 ◽  
Vol 149 (2) ◽  
pp. 352-357 ◽  
Author(s):  
Mitsuyasu Hashimoto ◽  
Takayuki Hibi ◽  
Atsushi Noma
Keyword(s):  
Distributive Lattices ◽  
Semigroup Rings ◽  
Class Groups ◽  
Divisor Class ◽  
Affine Semigroup
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