The spectrum ?(G) of a finite group G is the set orders its elements. following sufficient criterion nonsolvability proved: if, among prime divisors order G, there are four different primes such that contains all their pairwise products but not product any three these numbers, then nonsolvable. Using this result, we show for q ? 8 and ? 32, direct square Sz(q) × simple exceptional Suzuki unique...

In a series of papers [17-19] Morava uses an infinite sequence of extraordinary K-theories to give an elegant structure theorem for the complex cobordism of a finite complex. Much of Morava's theory is embedded in a rather sophisticated algebraic setting. In our attempt to understand his work, we have found more conventional algebraic topological proofs of many of his results. Also, our approac...

Recently the first example of a family pro-p groups, for p prime, with full normal Hausdorff spectrum was constructed. In this paper we further investigate by computing their finitely generated respect to each five standard filtration series: p-power series, iterated lower p-series, Frattini series and dimension subgroup series. Here spectra these groups consist infinitely many p-adic rational ...

In this paper, we introduce a new generalization of weakly prime ideals called $I$-prime. Suppose $R$ is a commutative ring with identity and $I$ a fixed ideal of $R$. A proper ideal $P$ of $R$ is $I$-prime if for $a, b in R$ with $ab in P-IP$ implies either $a in P$ or $b in P$. We give some characterizations of $I$-prime ideals and study some of its properties.  Moreover, we give conditions  ...

We discuss the Bousfield localization LEX for any spectrum E and any HR-module X, where R is a ring with unit. Due to the splitting property of HR-modules, it is enough to study the localization of Eilenberg– MacLane spectra. Using general results about stable f -localizations, we give a method to compute the localization of an Eilenberg–MacLane spectrum LEHG for any spectrum E and any abelian ...

Let n ≥ 1 and let p be any prime. Also, let En be the LubinTate spectrum, Gn the extended Morava stabilizer group, and K(n) the nth Morava K-theory spectrum. Then work of Devinatz and Hopkins and some results due to Behrens and the first author of this note, show that if X is a finite spectrum, then the localization LK(n)(X) is equivalent to the homotopy fixed point spectrum (LK(n)(En ∧ X))hGn ...

One of the central problems of algebraic K-theory is to compute the K-groups KX of a scheme X. Since these groups are, by definition, the homotopy groups of a spectrum KX, it makes sense to analyze the homotopy-type of the spectrum, rather than just the disembodied homotopy groups. In addition to facilitating the computation of the K-groups themselves, knowledge of the spectrum KX can be applie...

 Prime submodules and artinian prime modules are characterized. Furthermore, some previous results on prime modules and second modules are generalized.

awareness of their environment and internal state, fulfills the need of dynamic spectrum access for higher spectrum utilization. However, at the same time, the use of cognitive radios further complicates the security problems in wireless networks and introduces additional challenges for a counter measure. Due to the intelligence of the attackers, many of the attacks may be stealthy by nature, s...

Cognitive radios (CRs) have been recently emerging as prime candidates to enhance spectral efficiency by exploiting spectrum-aware systems which can reliably monitor licensed users’ activities. CR users monitor such activities by performing spectrum sensing to detect potential white spaces. However, this process of local sensing might be a challenging task in fading environments. The inefficien...