Retrieving information about a group from its character degrees or from its class sizes

Retrieving Information about a Group from Its Character Degrees or from Its Class Sizes

We prove that a knowledge of the character degrees of a finite group G and of their multiplicities determines whether G has a Sylow p-subgroup as a direct factor. An analogous result based on a knowledge of the conjugacy class sizes was known. We prove variations of both results and discuss their similarities.

Determining a Semisimple Group from its Representation Degrees

The Lie algebra of a compact semisimple Lie group G is determined by the degrees of the irreducible representations of G. However, two different groups can have the same representation degrees.

Fixed Point Spaces, Primitive Character Degrees and Conjugacy Class Sizes

f/sla from learner perspectives: a social activity or a cognitive process

in the past couple of decades sociocultural theory of sla and its implications in efl contexts have attracted attentions of research circles worldwide and aroused some controversies. firth and wagner (1997) have questioned the principles of the cognitive view which gives importance to mental constructs in favor of sociocultural view which highlights social and contextual constructs. but if soci...

Retrieving information from subordination

We show that if (Xs, s ≥ 0) is a right-continuous process, Yt = ∫ t 0 dsXs its integral process and τ = (τl, l ≥ 0) a subordinator, then the time-changed process (Yτl , l ≥ 0) allows to retrieve the information about (Xτl , l ≥ 0) when τ is stable, but not when τ is a gamma subordinator. This question has been motivated by a striking identity in law involving the Bessel clock taken at an indepe...