I'd suggest a look at (from pp.14-15 pdf):

Another vulnerability of Zawahiri is his attacks and abject hatred of the Muslim Brotherhood, that found its ultimate expression in a 1994 book “Bitter Harvest.” Zawahiri attacks the Muslim Brotherhood, Hamas and Hizballah for working with the government and participating in electoral politics. This only serves to further isolate al-Qaida and Zawahiri from the wider Islamist movement.
Ayman al-Zawahiri, A Mythic Figure or Fringe Leader within the Islamist Political Movement: Highlighting the 2006 Writings of Egyptian Journalist Gamal Abdal-Rahim (by LCDR Youssef Aboul-Enein, MSC, USN 2006) (15 pages pdf).

This is a book review, not a scholarly thesis; but it points up the links and disputes that now-target #1 had with the various factions and affiliated groups of the Egyptian MB.

While collateral to Zawahiri's relationship to EGB, I think this comment by LCDR Aboul-Enein (pp.13-14 pdf) is worth some present thought (emphasis added):

Another disagreement I have with the book is the insistence that the term al-Qaida was derived from the string of five Afghan bases (Farouk, Badr, Jalalabad, al-Siddiq and Jihad), it is most likely the name was derived from Azzam’s many speeches and writings calling for the establishment of al-Qaida al-Sulba (firm foundation). The language of Islamist militants is important, as base and foundation are two different entities, with a foundation connoting flexibility that ranges from base to a transnational world of global logistical support.
The wider "base-foundation" concept is somewhat similar to our (US) concept of a special operations base, which can have more than one geographic location so long as the functional components are networked.

I'd hope that the above is useful for educational, not argumentative, purposes.

Regards

Mike