Yeah, that wiki article is confusing. Broadcom Inc is the new company formed when Avago purchased Broadcom Corp, and Avago got it's start as a spin off of HP (by way of Agilent). However, the original Broadcom Corp is older than that and was unrelated to HP:
It took me a couple of readings to get that right. Yes, it is confusing.
Part of me thinks that corporate acquisitions and mergers should not be permitted to use prior names, and especially not to adopt the name of an earlier, non-ancestor parent.
https://en.wikipedia.org/wiki/Broadcom_Corporation