Let $N$ be a submodule of a module $M$ and a minimal primary decomposition of $N$ is known‎. ‎A formula to compute Baer's lower nilradical of $N$ is given‎. ‎The relations between classical prime submodules and their nilradicals are investigated‎. ‎Some situations in which semiprime submodules can be written as finite intersection of classical prime submodule are stated‎.

Given a maximal finite subgroup G of the nth Morava stabilizer group at a prime p, we address the question: is the associated higher real K-theory EOn a summand of the K(n)-localization of a TAF-spectrum associated to a unitary similitude group of type U(1, n − 1)? We answer this question in the affirmative for p ∈ {2, 3, 5, 7} and n = (p − 1)pr−1 for a maximal finite subgroup containing an ele...

Let c ≥ 0, d ≥ 2 be integers and N (d) c be the variety of groups in which every dgenerator subgroup is nilpotent of class at most c. N.D. Gupta posed this question that for what values of c and d it is true that N (d) c is locally nilpotent? We prove that if c ≤ 2 d + 2 − 3 then the variety N (d) c is locally nilpotent and we reduce the question of Gupta about the periodic groups in N (d) c to...

let $n$ be a submodule of a module $m$ and a minimal primary decomposition of $n$ is known‎. ‎a formula to compute baer's lower nilradical of $n$ is given‎. ‎the relations between classical prime submodules and their nilradicals are investigated‎. ‎some situations in which semiprime submodules can be written as finite intersection of classical prime submodule are stated‎.

Abstract We prove that a group homomorphism ? : L ? G \varphi\colon L\to G from locally compact Hausdorff ???? into discrete ???? either is continuous, or there exists normal open subgroup N ? N\subseteq L such ?</m:m...

Much has been written about component groups of Néron models of Jacobians of modular curves. In a variety of contexts, these groups have been shown to be “Eisenstein,” which implies that they can be neglected in the study of irreducible two-dimensional representations of Gal(Q/Q). The first theorem to this effect may be extracted from Mazur’s landmark article [11], which concerns the Jacobian J...

let $g={rm sl}_2(p^f)$ be a special linear group and $p$ be a sylow‎ ‎$2$-subgroup of $g$‎, ‎where $p$ is a prime and $f$ is a positive‎ ‎integer such that $p^f>3$‎. ‎by $n_g(p)$ we denote the normalizer of‎ ‎$p$ in $g$‎. ‎in this paper‎, ‎we show that $n_g(p)$ is nilpotent (or‎ ‎$2$-nilpotent‎, ‎or supersolvable) if and only if $p^{2f}equiv‎ ‎1,({rm mod},16)$‎.

We show that, for all characteristic p global fields k and natural numbers n coprime to the order of the non–p–part of the Picard group Pic0(k) of k, there exists an abelian extension L/k whose local degree at every prime of k is equal to n. This answers in the affirmative in this context a question recently posed by Kisilevsky and Sonn. As a consequence, we show that, for all n and k as above,...

Let p be a prime number and let n an integer not divisible by such that every group of order np has normal subgroup p. (This holds in particular for p>n.) Under these hypotheses, we obtain one-to-one correspondence between the isomorphism classes braces size set pairs (Bn,[τ]), where Bn runs over [τ] morphisms from multiplicative to Zp⁎ under certain equivalence relation. This gives classificat...

‎let $g$ be a finite group‎. ‎in [ghasemabadi et al.‎, ‎characterizations of the simple group ${}^2d_n(3)$ by prime graph‎ ‎and spectrum‎, ‎monatsh math.‎, ‎2011] it is‎ ‎proved that if $n$ is odd‎, ‎then ${}^2d _n(3)$ is recognizable by‎ ‎prime graph and also by element orders‎. ‎in this paper we prove‎ ‎that if $n$ is even‎, ‎then $d={}^2d_{n}(3)$ is quasirecognizable by‎ ‎prime graph‎, ‎i.e‎...