Clifford theory for p-sections of finite groups

Clifford Periodicity from Finite Groups

We deduce the periodicity 8 for the type of Pin and Spin representations of the orthogonal groups O(n) from simple combinatorial properties of the finite Clifford groups generated by the gamma matrices. We also include the case of arbitrary signature O(p, q). The changes in the type of representation can be seen as a rotation in the complex plane. The essential result is that adding a (+) dimen...

FINITE p-GROUPS IN REPRESENTATION THEORY

Finite gap theory of the Clifford torus

In this paper we construct the spectral curve and the Baker–Akhiezer function for the Dirac operator which form the data of the Weierstrass representation of the Clifford torus. This torus appears in many conjectures from differential geometry (see Section 2). By constructing this Baker–Akhiezer function we demonstrate a general procedure for constructing Dirac operators and their Baker–Akhieze...

Finite Groups with p-Sylow Coverings

Pairwise‎ ‎non-commuting elements in finite metacyclic $2$-groups and some finite $p$-groups

Let $G$ be a finite group‎. ‎A subset $X$ of $G$ is a set of pairwise non-commuting elements‎ ‎if any two distinct elements of $X$ do not commute‎. ‎In this paper‎ ‎we determine the maximum size of these subsets in any finite‎ ‎non-abelian metacyclic $2$-group and in any finite non-abelian $p$-group with an abelian maximal subgroup‎.