On finite pp-groups whose automorphisms are all central

An automorphism $\alpha$ of a group $G$ is said to be central if $\alpha$ commutes with every inner automorphism of $G$. We construct a family of non-special finite $p$-groups having abelian automorphism groups. These groups provide counter examples to a conjecture of A. Mahalanobis [Israel J. Math., {\bf 165} (2008), 161 - 187]. We also construct a family of finite $p$-groups having non-abelian automorphism groups and all automorphisms central. This solves a problem of I. Malinowska [Advances in group theory, Aracne Editrice, Rome 2002, 111-127].Comment: 11 pages, Counter examples to a conjecture from [Israel J. Math., {\bf 165} (2008), 161 - 187]; This paper will appear in Israel J. Math. in 201

A survey on pairwise mutually permutable products of finite groups

In this paper we present some recent results about pairwise mutually permutable products and classes of groups related to the saturated formation of all supersoluble groups

S-Embedded subgroups in finite groups

In this survey paper several subgroup embedding properties related to permutability are introduced and studied

Structure of an archaeal PCNA1-PCNA2-FEN1 complex: elucidating PCNA subunit and client enzyme specificity.

The archaeal/eukaryotic proliferating cell nuclear antigen (PCNA) toroidal clamp interacts with a host of DNA modifying enzymes, providing a stable anchorage and enhancing their respective processivities. Given the broad range of enzymes with which PCNA has been shown to interact, relatively little is known about the mode of assembly of functionally meaningful combinations of enzymes on the PCNA clamp. We have determined the X-ray crystal structure of the Sulfolobus solfataricus PCNA1-PCNA2 heterodimer, bound to a single copy of the flap endonuclease FEN1 at 2.9 A resolution. We demonstrate the specificity of interaction of the PCNA subunits to form the PCNA1-PCNA2-PCNA3 heterotrimer, as well as providing a rationale for the specific interaction of the C-terminal PIP-box motif of FEN1 for the PCNA1 subunit. The structure explains the specificity of the individual archaeal PCNA subunits for selected repair enzyme 'clients', and provides insights into the co-ordinated assembly of sequential enzymatic steps in PCNA-scaffolded DNA repair cascades

Prefactorized subgroups in pairwise mutually permutable products

The final publication is available at Springer via http://dx.doi.org/10.1007/s10231-012-0257-yWe continue here our study of pairwise mutually and pairwise totally permutable products. We are looking for subgroups of the product in which the given factorization induces a factorization of the subgroup. In the case of soluble groups, it is shown that a prefactorized Carter subgroup and a prefactorized system normalizer exist.Aless stringent property have F-residual, F-projector and F-normalizer for any saturated formation F including the supersoluble groups.The first and fourth authors have been supported by the grant MTM2010-19938-C03-01 from MICINN (Spain).Ballester-Bolinches, A.; Beidleman, J.; Heineken, H.; Pedraza Aguilera, MC. (2013). Prefactorized subgroups in pairwise mutually permutable products. Annali di Matematica Pura ed Applicata. 192(6):1043-1057. https://doi.org/10.1007/s10231-012-0257-yS104310571926Amberg B., Franciosi S., de Giovanni F.: Products of Groups. Clarendon Press, Oxford (1992)Ballester-Bolinches, A., Pedraza-Aguilera, M.C., Pérez-Ramos, M.D.: Totally and Mutually Permutable Products of Finite Groups, Groups St. Andrews 1997 in Bath I. London Math. Soc. Lecture Note Ser. 260, 65–68. Cambridge University Press, Cambridge (1999)Ballester-Bolinches A., Pedraza-Aguilera M.C., Pérez-Ramos M.D.: On finite products of totally permutable groups. Bull. Aust. Math. Soc. 53, 441–445 (1996)Ballester-Bolinches A., Pedraza-Aguilera M.C., Pérez-Ramos M.D.: Finite groups which are products of pairwise totally permutable subgroups. Proc. Edinb. Math. Soc. 41, 567–572 (1998)Ballester-Bolinches A., Beidleman J.C., Heineken H., Pedraza-Aguilera M.C.: On pairwise mutually permutable products. Forum Math. 21, 1081–1090 (2009)Ballester-Bolinches A., Beidleman J.C., Heineken H., Pedraza-Aguilera M.C.: Local classes and pairwise mutually permutable products of finite groups. Documenta Math. 15, 255–265 (2010)Beidleman J.C., Heineken H.: Mutually permutable subgroups and group classes. Arch. Math. 85, 18–30 (2005)Beidleman J.C., Heineken H.: Group classes and mutually permutable products. J. Algebra 297, 409–416 (2006)Carocca A.: p-supersolvability of factorized groups. Hokkaido Math. J. 21, 395–403 (1992)Carocca, A., Maier, R.: Theorems of Kegel-Wielandt Type Groups St. Andrews 1997 in Bath I. London Math. Soc. Lecture Note Ser. 260, 195–201. Cambridge University Press, Cambridge, (1999)Doerk K., Hawkes T.: Finite Soluble Groups. Walter De Gruyter, Berlin (1992)Maier R., Schmid P.: The embedding of quasinormal subgroups in finite groups. Math. Z. 131, 269–272 (1973

Dynamic Disorder in Quasi-Equilibrium Enzymatic Systems

Conformations and catalytic rates of enzymes fluctuate over a wide range of timescales. Despite these fluctuations, there exist some limiting cases in which the enzymatic catalytic rate follows the macroscopic rate equation such as the Michaelis-Menten law. In this paper we investigate the applicability of macroscopic rate laws for fluctuating enzyme systems in which catalytic transitions are slower than ligand binding-dissociation reactions. In this quasi-equilibrium limit, for an arbitrary reaction scheme we show that the catalytic rate has the same dependence on ligand concentrations as obtained from mass-action kinetics even in the presence of slow conformational fluctuations. These results indicate that the timescale of conformational dynamics – no matter how slow – will not affect the enzymatic rate in quasi-equilibrium limit. Our numerical results for two enzyme-catalyzed reaction schemes involving multiple substrates and inhibitors further support our general theory

Nurse-patient interaction and communication: a systematic literature review

Aim: The purpose of this review is to describe the use and definitions of the concepts of nurse-patient interaction and nurse-patient communication in nursing literature. Furthermore, empirical findings of nurse-patient communication research will be presented, and applied theories will be shown. Method: An integrative literature search was executed. The total number of relevant citations found was 97. The search results were reviewed, and key points were extracted in a standardized form. Extracts were then qualitatively summarized according to relevant aspects and categories for the review. Results: The relation of interaction and communication is not clearly defined in nursing literature. Often the terms are used interchangeably or synonymously, and a clear theoretical definition is avoided or rather implicit. Symbolic interactionism and classic sender-receiver models were by far the most referred to models. Compared to the use of theories of adjacent sciences, the use of original nursing theories related to communication is rather infrequent. The articles that try to clarify the relation of both concepts see communication as a special or subtype of interaction. Conclusion: The included citations all conclude that communication skills can be learned to a certain degree. Involvement of patients and their role in communication often is neglected by authors. Considering the mutual nature of communication, patients’ share in conversation should be taken more into consideration than it has been until now. Nursing science has to integrate its own theories of nursing care with theories of communication and interaction from other scientific disciplines like sociology

Sections of Angles and n-th Roots of Numbers

It is known since Galois that an algebraic equation can be solved using suitable n-th roots whenever the corresponding Galois group is soluble. The object of this note is to construct real numbers with the use of the n-th parts of suitable angles and to state necessary and sufficient conditions for this to be possible.Від Галуа відомо, що алгебраїчне рівняння можна розв'язані за допомогою n-х коренів щоразу, коли відповідна група Галуа с розв'язною. Метою даної статті є побудова дійсних чисел за допомогою n-х частин відповідних кутів та встановлення необхідної і достатньої умови, коли це можливо