We define an extension L/K of absolutely abelian number fields to be Leopoldt if the ring of integers OL of L is free as a module over the associated order AL/K of L/K. Furthermore, we say that an abelian number field K is Leopoldt if every extension L/K with L/Q abelian is Leopoldt. In this paper, we make progress towards a classification of Leopoldt number fields and extensions. The two main ...

given a non-abelian finite group $g$, let $pi(g)$ denote the set of prime divisors of the order of $g$ and denote by $z(g)$ the center of $g$. thetextit{ prime graph} of $g$ is the graph with vertex set $pi(g)$ where two distinct primes $p$ and $q$ are joined by an edge if and only if $g$ contains an element of order $pq$ and the textit{non-commuting graph} of $g$ is the graph with the vertex s...

the increasing number of scientific journals, even in a subfield, necessitates a reliable and authoritative measure for researchers and libraries to identify core journals in a given subfield. the impact factor value is affected by different factors such as subject area, type of documents or length of the citation measurement window. in order to prioritize the choice of quality journals for sci...

Introduction We present, for the first time, functional activation patterns within hippocampal subfields in temporal lobe epilepsy (TLE) patients. The hippocampus is a complex structure consisting of subregions that express varied cell types, and are differentially affected by neurological disorders, including TLE. For example, dentate gyrus (DG) is one subfield that has been implicated in both...

Let k be an arbitrary field. We study a general method to solve the subfield problem of generic polynomials for the symmetric groups over k via Tschirnhausen transformation. Based on the general result in the former part, we give an explicit solution to the field isomorphism problem and the subfield problem of cubic generic polynomials for S3 and C3 over k. As an application of the cubic case, ...