The purpose of the present paper is to consider the notion of isoclinism between two finite groups and its generalization to n-isoclinism, introduced by J. C. Bioch in 1976. A weaker form of n-isoclinism, called relative n-isoclinism, will be discussed. This will allow us to improve some classical results in literature. We will point out the connections between a relative n-isoclinism and the notions of commutativity degree, n-th nilpotency degree and relative n-th nilpotency degree, which arouse interest in the classification of groups of prime power order in the last years.
The $R_\infty$-nilpotency degree of some lollipop GBS groups
UFES – Universidade Federal do Espírito Santo（圣埃斯皮里图联邦大学）；IFSP – Instituto Federal de São Paulo（圣保罗联邦理工学院）；UFSCar – Universidade Federal de São Carlos（圣卡洛斯联邦大学）
The Orbit Method for Finite Groups of Nilpotency Class Two of Odd Order
首先，构造了具有2-可分中心的幂零类2的（拓扑）群与具有2-可分中心的幂零类2的（拓扑）李环之间的同构。这种同构允许我们像往常一样构造伴随表示和余伴随表示。对于奇阶幂零类2的有限群G，在其群代数C[G]中构造一个基，用g* 的元素参数化，使得余伴随轨道的元素构成C[G]的简单双边理想的基.这种构造给出了g* 中的G-轨道与G的不可约酉表示的等价类之间的一一对应，这意味着一个非常简单的特征标公式。该对应的性质类似于由幂零连通和单连通李群的基里洛夫轨道方法给出的类似对应的性质。在我的文章“Diagrams of Representations，math.RT/9803079（1998）”和我的论文“A Combinatorial Approach to Representations of李群and Algebras，University of Pennsylvania（1998）”中介绍的图方法为我们研究轨道上的正规形和相应的表示提供了一种方便的方法。
On the representation dimension of finite $p$-groups
Indian Institute of Technology Ropar（印度技术学院罗帕尔分校）；Indian Institute of Science Education and Research Mohali（印度科学教育研究学院莫哈里分校）；SRM Institute of Science and Technology（SRM科学与技术学院）
