Representaions of Path Algebras with Applications to Subgroup Lattices and Group Characters(jointly worked)

Iiyori Nobuo and Masato Sawabe

Tokyo Journal of Mathematics 37(1) 37-59 2014 [Refereed]

Let be a quiver, and a weight function on the set of arrows of . In this paper, we will introduce an -algebra over a ring in which the information how vertices of are joined by its arrows with weights should be r...

Simplicial complexes associated to quivers arising from finite groups(jointly worked)

Nobuo Iiyori, Masato Sawabe

Osaka journal of mathematics ５２(1) １６１-２０４ Jan 2015 [Refereed]

In this paper, we will introduce a simplicial complex defined by a quiver and a family of paths in . We call a path complex of in . Let be a finite group, and denote by and ${\rm Co...

Partially ordered sets of non-trivial nilpotent -subgroups.

Sawabe, Masato

Osaka Journal of Mathematics 53(3) 731-750 Jul 2016 [Refereed]

We introduce a subposet of a poset of all non-trivial nilpotent -subgroups of a finite group . We examine basic properties of a subgroup in which contains the notion of both a radical -subgro...

A New Characterization of Some Simple Groups by Order and Degree Pattern of Solvable Graph.

B. Akbari, A. R. Moghaddamfar

A New Characterization of Some Simple Groups by Order and Degree Pattern of Solvable Graph 45(3) 337-363 Nov 2016 [Refereed]

The solvable graph of a finite group , denoted by&0a;, is a simple graph whose vertices are the prime divisors of and two distinct primes and are joined by an edge if and only if there exists a solvable subgro...

Homology of a certain associative algebra(jointly worked)

４６(１) １-３０ 2017 [Refereed]

Let A be a associative R-algebra posessing an R-basis B. We introduce a homology H_n (A,B) and we develop a general theory of H_n (A,B). Some example of H_n (A,B) are also provided.