a $p$-group $g$ is called a $mathcal{cac}$-$p$-group if $c_g(h)/h$ is ‎cyclic for every non-cyclic abelian subgroup $h$ in $g$ with $hnleq‎ ‎z(g)$‎. ‎in this paper‎, ‎we give a complete classification of‎ ‎finite $mathcal{cac}$-$p$-groups‎.

PURPOSE To propose and evaluate P-LORAKS a new calibrationless parallel imaging reconstruction framework. THEORY AND METHODS LORAKS is a flexible and powerful framework that was recently proposed for constrained MRI reconstruction. LORAKS was based on the observation that certain matrices constructed from fully sampled k-space data should have low rank whenever the image has limited support o...

Some problems on algebraic groups over global fields like the congruence subgroup problem involve the determination of topological central extensions of the adelic group which, in turn, leads naturally to the study of topological central extensions of p-adic Lie groups by finite groups like the group of roots of unity in the p-adic field. Moreover, central extensions of semisimple p-adic Lie gr...

We conjecture that, for a fixed prime $p$, rational elliptic curves with higher rank tend to have more points mod $p$. show that there is an analogous bias modular forms respect root numbers, and the order of greater than number forms.

We construct an infinite set of retractions from certain loop spaces of suspended low rank CW -complexes X localized at an odd prime p. These retracts are themselves loop spaces of arbitrary suspensions of X. This is accomplished with the help of modular representations and their applications to topology.

If R is a valuation domain of maximal ideal P with a maximal immediate extension of finite rank it is proven that there exists a finite sequence of prime ideals P = L0 ⊃ L1 ⊃ · · · ⊃ Lm ⊇ 0 such that RLj /Lj+1 is almost maximal for each j, 0 ≤ j ≤ m − 1 and RLm is maximal if Lm 6= 0. Then we suppose that there is an integer n ≥ 1 such that each torsion-free R-module of finite rank is a direct s...