A non-abelian 2-group whose endomorphisms generate a ring, and other examples of E-groups
Groups for which the distributively generated near-ring generated by the endomorphisms is in fact a ring are known as E-groups and are discussed in (3). R. Faudree in (1) has given the only published examples of non-abelian E-groups by presenting defining relations for a family of p–groups. However, as shown in (3), Faudree's group does not have the desired property when p = 2.
More on groups in which each element commutes with its endomorphic images
R. Faudree has given examples of nonabelian groups which have the property cited in the title. His groups are p-groups such that (i) Z(G) = G'= GP= U(G), (ii) each endomorphism 0 (which is not an automorphism) has (G)qs < Z(G), and (iii) each automorphism is central. In this paper the necessity of these conditions is explored. It is also shown that, for p = 2, Faudree's example does not in fact have the property cited in the title.
Speci fi cation Test for Panel Data Models with Interactive Fixed E ff ects ∗
In this paper, we propose a consistent nonparametric test for linearity in a large dimensional panel data model with interactive fixed effects. Both lagged dependent variables and conditional heteroskedasticity of unknown form are allowed in the model. We estimate the model under the null hypothesis of linearity to obtain the restricted residuals which are then used to construct the test statistic. We show that after being appropriately centered and standardized, the test statistic is asymptotically normally distributed under both the null hypothesis and a sequence of Pitman local alternatives by using the concept of conditional strong mixing that was recently introduced by Prakasa Rao (2009). To improve the finite sample performance, we propose a bootstrap procedure to obtain the bootstrap -value. A small set of Monte Carlo simulations illustrates that our test performs well in finite samples. An application to an economic growth panel dataset indicates significant nonlinear relationships between economic growth, initial income level and capital accumulation.