A Robinson characterization of finite PσTP\sigma T-groups

Let $\sigma =\{\sigma_{i} | i\in I\}$ be some partition of the set of all primes $\Bbb{P}$ and let $G$ be a finite group. Then $G$ is said to be $\sigma$-full if $G$ has a Hall $\sigma _{i}$-subgroup for all $i$. A subgroup $A$ of $G$ is said to be $\sigma$-permutable in $G$ provided $G$ is $\sigma$-full and $A$ permutes with all Hall $\sigma _{i}$-subgroups $H$ of $G$ (that is, $AH=HA$) for all $i$. We obtain a characterization of finite groups $G$ in which $\sigma$-permutability is a transitive relation in $G$, that is, if $K$ is a ${\sigma}$-permutable subgroup of $H$ and $H$ is a ${\sigma}$-permutable subgroup of $G$, then $K$ is a ${\sigma}$-permutable subgroup of $G$.Comment: 15 pages. arXiv admin note: text overlap with arXiv:1704.0250

On Linear Maps and Seed Sets of Beidleman Near-Vector Spaces

We studied linear mappings in Beidleman near-vector spaces and explored their matrix representations using $R$-bases of $R$-subgroups. Additionally, we developed algorithms for determining the seed number and seed sets of $R$-subgroups within finite-dimensional Beidleman near-vector spaces.Comment: arXiv admin note: text overlap with arXiv:1810.0722

MS-124: Samuel Simon Schmucker Bicentennial Celebration 1999

The official papers of the Schmucker Bicentennial Committee reside in the Archives at the Lutheran Theological Seminary at Gettysburg. This collection at the college contains the material retained by Gettysburg College representatives to the committee and internal college documents relating to the program events compiled by the Public Relations Office and the Office of Planned Giving. Of special interest is a review of a research effort conducted within the Office of College Relations to identify the descendants of Samuel Schmucker in order to invite them to the college for the birthday event. This research resulted in the creation of a large family genealogical chart containing the names of 131 descendent of Schmucker. The collection contains correspondence with and personal histories of some of the living descendants. Special Collections and College Archives Finding Aids are discovery tools used to describe and provide access to our holdings. Finding aids include historical and biographical information about each collection in addition to inventories of their content. More information about our collections can be found on our website http://www.gettysburg.edu/special_collections/collections/.https://cupola.gettysburg.edu/findingaidsall/1112/thumbnail.jp

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

A framework for the classification of accounts manipulations

Accounts manipulations have been a matter of research, discussion and, even, controversy in several countries such as the United States, Canada, the United Kingdom, Australia and France. The objective of this paper is to elaborate a general framework for classifying accounts manipulations through a thorough review of the literature. This framework is based on the desire to influence the market participants' perception of the risk associated to the firm. The risk is materialized through the earnings per share and the debt/equity ratio. The literature on this topic is already very rich, although we have identified series of areas in need for further research.accounts manipulations; earnings management; income smoothing; big bath accounting; creative accounting