PROJECTIVE CHARACTERS WITH PRIME POWER DEGREES

We consider the relationship between structural information of a finite group $G$ and $\text{cd}_{\unicode[STIX]{x1D6FC}}(G)$, the set of all irreducible projective character degrees of $G$ with factor set $\unicode[STIX]{x1D6FC}$. We show that for nontrivial $\unicode[STIX]{x1D6FC}$, if all numbers in $\text{cd}_{\unicode[STIX]{x1D6FC}}(G)$ are prime powers, then $G$ is solvable. Our result is proved by classical character theory using the bijection between irreducible projective representations and irreducible constituents of induced representations in its representation group.

Matricial Representations of Certain Finitely Presented Groups Generated by Order-2 Generators and Their Applications

In this paper, we study matricial representations of certain finitely presented groups Γ2Nwith N-generators of order-2. As an application, we consider a group algebra A2 of Γ22; under our representations. Specifically, we characterize the inverses g-1of all group elements g in Γ22; in terms of matrices in the group algebra A2. From the study of this characterization, we realize there are close relations between the trace of the radial operator of A2; and the Lucas numbers appearing in the Lucas triangle. KEYWORDS: Matricial Representation; Group Presentation; Group Algebras; Lucas Numbers; Lucas Triangle; Finitely Presented Group;Group Relations; Free Probability

Writing as survival

This chapter examines the writing of Over the Water (first published in 1987) as a process of exploration, commemoration and resistance. It considers the narratives of a second generation Irish teenager and her mother, each constrained by the context of Britain’s occupation of Ireland and resultant attacks on the civil liberties of Irish people in Britain. Noting the importance of second wave feminism and the development of women’s presses in generating resistance to these constraints, it also considers the empowering role of the Irish in Britain Representation Group (IBRG). It celebrates the writing of fiction as a process of surviving and thriving, using the transformative power of language to imagine new spaces of resistance and hope.

The Role of Rules in Representation: Group Membership and Electoral Incentives

Existing research shows that the election of members of previously underrepresented groups can have significant consequences for policymaking. Yet, quotas, reserved seats, communal rolls, and race-conscious districting make it difficult to distinguish whether it is group membership, electoral incentives, or a combination of the two that matters. It is argued here that lawmakers who are members of underrepresented groups will stand out as defenders of their group’s interests only when electoral rules incentivize them to do so. This is demonstrated empirically using data from New Zealand, showing that Māori Members of Parliament systematically vary in the extent to which they represent their ethnic group as a function of the three different sets of rules under which they were elected.

Clustering Based on NMTF Algorithm

NMTF(Normalizing Mapping Training Framework) operates by mapping initial cluster centers and then iteratively training points to clusters base on the proximate cluster center and updating cluster centers. we regard finding good cluster centers as a normalizing parameter estimation problem then constructing the parameters of other normalizing models yields a space of novel clustering methods. In this paper we propose the idea using abstract of a text to members of a data partition in place of estimation of cluster centers. The method can accurately reconstruct meaning representation group used to generate a given data set.

THE BAD BEHAVIOR OF REPRESENTATION GROUPS

Let (H, A) be a primitive central extension of a finite group G. We show that A is not characteristic in H in general, and further demonstrate in a series of examples that results, which hold about inner automorphisms of H, do not extend to the full automorphism group of H. We also give some new results about isoclinism and representation groups of G in the case that H is capable. Finally we give an example of two non-isomorphic groups of the same order, which not only have a representation group in common, but also have identical projective character tables.