Irreducible character degrees and normal subgroups

Let N be a normal subgroup of a finite group G and consider the set cd(G|N) of degrees of irreducible characters of G whose kernels do not contain N. A number of theorems are proved relating the set cd(G|N) to the structure of N. For example, if N is solvable, its derived length is bounded above by a function of |cd(G|N)|. Also, if |cd(G|N)| is at most 2, then N is solvable and its derived length is at most |cd(G|N)|. If G is solvable and |cd(G|N)| = 3, then the derived length of N is at most 3

Unemployment Insurance: Legislative Issues in the 113th Congress

The 113th Congress may face a number of issues related to currently available unemployment insurance programs: Unemployment Compensation (UC), temporary Emergency Unemployment Compensation (EUC08), and Extended Benefits (EB). With the national unemployment rate decreasing but still high, the weekly demand for extended unemployment benefits continues at elevated levels. Congress deliberated multiple times on whether to extend the authorization for several key temporary unemployment insurance provisions in the 112th Congress and may do so again in the 113th Congress. The signing of P.L. 112-240 on January 2, 2013, now means that the EUC08 program expires the week ending on or before January 1, 2014. The 100% federal financing of the EB program expires on December 31, 2013. In addition, the option for states to use three-year EB trigger lookbacks (the period of time considered in determining an active EB program within a state) expires the week ending on or before December 31, 2013. The 113th Congress will face these expirations as well as likely unemployment insurance policy issues, including unemployment insurance financing, integrity measures, and the appropriate length and availability of unemployment benefits. This report provides a brief overview of the three unemployment insurance programs—UC, EUC08, and EB—that may currently pay benefits to eligible unemployed workers. This report contains a brief explanation of how the EUC08 program, as well as some other UC-related payments, began to experience reductions in benefits as a result of the sequester order contained within the Budget Control Act of 2011 (P.L. 112-25). This report also includes descriptions of the unemployment insurance provisions within H.R. 51, H.R. 188, H.R. 1172, H.R. 1229, H.R. 1277, H.R. 1502, H.R. 1530, H.R. 1617, H.R. 2177, H.R. 2448, H.R. 2821, H.R. 2826, H.R. 2889, S. 18, S. 803, and S. 1099, as well as the President’s Budget Proposal for FY2014

Real fields and repeated radical extensions

The main result of this paper is that if E is a field extension of finite odd degree over a real field Q, and if E is a repeated radical extension of Q, then every intermediate field is also a repeated radical extension of Q. This paper also contains a number of other results about repeated radical extensions

The Fundamentals of Unemployment Compensation

[Excerpt] The joint federal-state Unemployment Compensation (UC) program provides income support through UC benefit payments. Although there are broad requirements under federal law regarding UC benefits and financing, the specifics are set out under each state’s laws. States administer UC benefits with U.S. Department of Labor (DOL) oversight, resulting in 53 different UC programs operated in the states, the District of Columbia, Puerto Rico, and the Virgin Islands. Total UC expenditures include benefits and administrative costs. During economic expansions, states fund approximately 85%-90% of all UC expenditures—as almost all of the benefits are state-financed by state unemployment taxes. In comparison, federal expenditures are relatively small during these expansions (approximately 10%-15%) in which federal expenditures are primarily administrative grants to the states financed by federal unemployment taxes

Unemployment Insurance: Programs and Benefits

[Excerpt] A variety of benefits may be available to unemployed workers to provide them with income support during a spell of unemployment. The cornerstone of this income support is the joint federal-state Unemployment Compensation (UC) program, which may provide income support through the payment of UC benefits for up to a maximum of 26 weeks. Other programs that may provide workers with income support are more specialized. They may target special groups of workers, be automatically triggered by certain economic conditions, be temporarily created by Congress with a set expiration date, or target typically ineligible workers through a disaster declaration. UC benefits may be extended at the state level by the permanent Extended Benefit (EB) program if high unemployment exists within the state. Once regular unemployment benefits are exhausted, the EB program may provide up to an additional 13 or 20 weeks of benefits, depending on worker eligibility, state law, and economic conditions in the state. The EB program is funded 50% by the federal government and 50% by the states, although the 2009 stimulus package (P.L. 111-5, as amended) temporarily provides for 100% federal funding of the EB program. A temporary unemployment insurance program, the Emergency Unemployment Compensation (EUC08) program, began in July 2008. The authorization for the EUC08 program expires the week ending on or before January 1, 2014. Therefore, the last day of EUC08 availability is December 28, 2013 (December 29, 2013, for New York). This was the eighth temporary program Congress has created to provide extended unemployment compensation during an economic slowdown. The EUC08 benefit is 100% federally funded. State UC agencies administer the EUC08 benefit along with regular UC benefits. See Appendix A for diagrams of the current unemployment benefits available to workers as well as a detailed diagram of the expansions and contractions of the EUC08 benefit. This report describes three kinds of unemployment benefits: regular UC, EB, and EUC08. The report explains their basic eligibility requirements, benefits, and financing structure

Unemployment Insurance: Legislative Issues in the 116th Congress

The unemployment insurance (UI) system has two primary objectives: (1) to provide temporary, partial wage replacement for involuntarily unemployed workers and (2) to stabilize the economy during recessions. In support of these goals, several UI programs provide benefits for eligible unemployed worker

Emergency Unemployment Compensation (EUC08): Current Status of Benefits

The temporary Emergency Unemployment Compensation (EUC08) program may provide additional federal unemployment insurance benefits to eligible individuals who have exhausted all available benefits from their state Unemployment Compensation (UC) programs. Currently, EUC08 benefits are available in all states except for North Carolina. Congress created the EUC08 program in 2008 and has amended the original, authorizing law (P.L. 110-252) 11 times. The most recent extension of EUC08 in P.L. 112-240, the American Taxpayer Relief Act of 2012, authorizes EUC08 benefits through the end of calendar year 2013. Under P.L. 112-240, the potential duration of EUC08 benefits available to eligible individuals depends on state unemployment rates. Figure A-1 provides the sequence, availability, and total maximum of all unemployment benefits. This report summarizes the structure of EUC08 benefits currently available through December 28, 2013 (December 29, 2013, for New York). It also provides the legislative history of the EUC08 program

Unemployment Insurance: Legislative Issues in the 115th Congress

[Excerpt] The 115th Congress continues to consider many issues related to the two major components of the unemployment insurance (UI) system: Unemployment Compensation (UC) and Extended Benefits (EB). This report provides short summaries of legislative proposals with respect to UI programs. It also gives a brief overview of the UI programs that may provide benefits to eligible unemployed workers. In addition, it briefly summarizes UI proposals included in the President’s budget for FY2018