Normality in a Kantor Family

Finite Groups that Admit Kantor Families

The basic problem of interest in this note is: What finite groups G admit a Kantor family (i.e., 4-gonal family) of subgroups? We begin with a survey of the known examples (of the groups G, not of the Kantor families) and then pose the question of whether or not two specific examples are isomorphic. The two groups in question have order q and coexist for q = 3 ≥ 27. Our conjecture had been that...

Parent/Child Concordance about Bullying Involvement and Family Characteristics Related to Bullying and Peer Victimization

MATHEMATICAL ENGINEERING TECHNICAL REPORTS Skewness and kurtosis as locally best invariant tests of normality

Consider testing normality against a one-parameter family of univariate distributions containing the normal distribution as the boundary, e.g., the family of t-distributions or an infinitely divisible family with finite variance. We prove that under mild regularity conditions, the sample skewness is the locally best invariant (LBI) test of normality against a wide class of asymmetric families a...

Skewness and kurtosis as locally best invariant tests of normality

Consider testing normality against a one-parameter family of univariate distributions containing the normal distribution as the boundary, e.g., the family of t-distributions or an infinitely divisible family with finite variance. We prove that under mild regularity conditions, the sample skewness is the locally best invariant (LBI) test of normality against a wide class of asymmetric families a...

Isomorphisms of groups related to flocks

A truly fruitful way to construct finite generalized quadrangles is through the detection of Kantor families in the general 5-dimensional Heisenberg group H2(q) over some finite field Fq . All these examples are so-called “flock quadrangles”. Payne (Geom. Dedic. 32:93–118, 1989) constructed from the Ganley flock quadrangles the new Roman quadrangles, which appeared not to arise from flocks, but...