TITLE: Holoedric isomorphism?
QUESTION [6 upvotes]: While trying to read the following article

Schottenfells, Ida May. Two Non-Isomorphic Simple Groups Of The Same Order 20,160.

I found the term "holoedrically isomorphic". In an abstract for the article, I also came across the claim that "Holoedric isomorphism is the only isomorphism that can exist between two simple groups." 
I haven't been able to find a definition for this term anywhere.  Presumably it is a stronger notion than that of a normal isomorphism of groups? What does it mean?

REPLY [7 votes]: Isomorphism did not used to mean 1-1, just onto. Holoedric isomorphisms are both 1-1 and onto. See page 381 of Burnside's Theory of Groups (1ed).  The standard english term was "simply isomorphic", the French term was isomorphisme holoédrique.
The corresponding term for non-injective epimorphism (so onto, not 1-1) was "multiply isomorphic" in English, and isomorphisme meriédrique in French.
"édrique" appears to be about the same as "edral" as in "dihedral".

Schottenfels, Ida May. "Two non-isomorphic simple groups of the same order 20,160."
Ann. of Math. (2) 1 (1899/00), no. 1-4, 147–152. 
MR1502265
DOI:10.2307/1967281