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41.
The commensurability index between two subgroups A,B of a group G is [A:A∩B][B:A∩B]. This gives a notion of distance among finite index subgroups of G, which is encoded in the p-local commensurability graphs of G. We show that for any metabelian group, any component of the p-local commensurabilty graph of G has diameter bounded above by 4. However, no universal upper bound on diameters of components exists for the class of finite solvable groups. In the appendix we give a complete classification of components for upper triangular matrix groups in GL(2,𝔽q). 相似文献
42.
Jesko Hüttenhain 《代数通讯》2017,45(9):3716-3723
We give a negative answer to a question by J. M. Landsberg on the nature of normalizations of orbit closures. A counterexample originates from the study of complex, ternary, cubic forms. 相似文献
43.
Artem N. Shevlyakov 《代数通讯》2017,45(9):3757-3767
A semigroup S is called an equational domain if any finite union of algebraic sets over S is algebraic. We give some necessary and su?cient conditions for a completely simple semigroup to be an equational domain. 相似文献
44.
Juping Tang 《代数通讯》2017,45(7):3017-3021
A subgroup A of a finite group G is called {1≤G}-embedded in G if for each two subgroups K≤H of G, where K is a maximal subgroup of H, A either covers the pair (K,H) or avoids it. Moreover, a subgroup H of G is called nearly m-embedded in G if G has a subgroup T and a {1≤G}-embedded subgroup C such that G?=?HT and H∩T≤C≤H. In this paper, we mainly prove that G is solvable if and only if its Sylow 3-subgroups, Sylow 5-subgroups and Sylow 7-subgroups are nearly m-embedded in G. 相似文献
45.
We investigate pointed Hopf algebras over finite nilpotent groups of odd order, with nilpotency class 2. For such a group G, we show that if its commutator subgroup coincides with its center, then there exists no non-trivial finite-dimensional pointed Hopf algebra with kG as its coradical. We apply these results to non-abelian groups of order p3, p4 and p5, and list all the pointed Hopf algebras of order p6, whose group of grouplikes is non-abelian. 相似文献
46.
Jairo Z. Goncalves 《代数通讯》2017,45(12):5193-5201
Let k(t) be the field of rational functions over the field k, let σ be a k-automorphism of K = k(t), let D = K(X;σ) be the ring of fractions of the skew polynomial ring K[X;σ], and let D? be the multiplicative group of D. We show that if N is a noncentral normal subgroup of D?, then N contains a free subgroup. We also prove that when k is algebraically closed and σ has infinite order, there exists a specialization from D to a quaternion algebra. This allows us to explicitly present free subgroups in D?. 相似文献
47.
In [1], Bannai presents a fusion condition and uses this to consider central Schur rings (S-rings) over the simple groups PSL(2,q) where q is a prime power. In this paper, we concretely describe all such S-rings in terms of symmetric S-rings over cyclic groups. The final section discusses counting these. 相似文献
48.
《Acta Crystallographica. Section C, Structural Chemistry》2017,73(7):575-581
Kryptoracemates are racemic compounds (pairs of enantiomers) that crystallize in Sohnke space groups (space groups that contain neither inversion centres nor mirror or glide planes nor rotoinversion axes). Thus, the two symmetry‐independent molecules cannot be transformed into one another by any symmetry element present in the crystal structure. Usually, the conformation of the two enantiomers is rather similar if not identical. Sometimes, the two enantiomers are related by a pseudosymmetry element, which is often a pseudocentre of inversion, because inversion symmetry is thought to be favourable for crystal packing. We obtained crystals of two kryptoracemates of two very similar compounds differing in just one residue, namely rac‐N‐[(1S ,2R ,3S )‐2‐methyl‐3‐(5‐methylfuran‐2‐yl)‐1‐phenyl‐3‐(pivalamido)propyl]benzamide, C27H32N2O3, (I), and rac‐N‐[(1S ,2S ,3R )‐2‐methyl‐3‐(5‐methylfuran‐2‐yl)‐1‐phenyl‐3‐(propionamido)propyl]benzamide dichloromethane hemisolvate, C25H28N2O3·0.5CH2Cl2, (II). The crystals of both compounds contain both enantiomers of these chiral molecules. However, since the space groups [P 212121 for (I) and P 1 for (II)] contain neither inversion centres nor mirror or glide planes nor rotoinversion axes, there are both enantiomers in the asymmetric unit, which is a rather uncommon phenomenon. In addition, it is remarkable that (II) contains two pairs of enantiomers in the asymmetric unit. In the crystal, molecules are connected by intermolecular N—H…O hydrogen bonds to form chains or layered structures. 相似文献
49.
《Macromolecular bioscience》2017,17(3)
In this contribution, amphiphilic star copolymers (H40‐star‐PCL‐a‐PEG) with an H40 hyperbranched polyester core and poly(ε‐caprolactone)‐a‐poly(ethylene glycol) copolymer arms linked with acetal groups are synthesized using ring‐opening polymerization and a copper (I)‐catalyzed alkyne‐azide cycloaddition click reaction. The acid‐cleavable acetal groups between the hydrophilic and hydrophobic segments of the arms endow the amphiphilic star copolymers with pH responsiveness. In aqueous solution, unimolecular micelles can be formed with good stability and a unique acid degradability, as is desirable for anticancer drug carriers. For the model drug of doxorubicin, the in vitro release behavior, intracellular release, and inhibition of proliferation of HeLa cells show that the acid‐cleavable unimolecular micelles with anticancer activity can be dissociated in an acidic environment and efficiently internalized by HeLa cells. Due to the acid‐cleavable and biodegradable nature, unimolecular micelles from amphiphilic star copolymers are promising for applications in intracellular drug delivery for cancer chemotherapy.
50.
Yutaka Yoshii 《代数通讯》2017,45(1):1-8
Let G be a connected, semisimple, and simply connected algebraic group defined and split over the finite field of order p, and let G(q) be the corresponding finite Chevalley or twisted group, where q = pr. Recently, Anwar determines the direct sum decomposition of the tensor product of the rth Steinberg module and a simple G-module with a (p,r)-minuscule highest weight λ. In this paper, we determine that of the tensor product regarded as a module for G(q) under some weak assumptions for λ. 相似文献