Geodesic
On Multiplicative Properties of Families of Complexes of Certain Loops
Canadian journal of mathematics, Tome 25 (1973) no. 5, pp. 1066-1077

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It is well-known that if is a quotient group of a group G, then (i) is a partition of G, and (ii) the usual complex product (in the usual sense of multiplication of complexes) of every pair of members of is a member of . There arises the question whether, conversely, (i) and (ii), perhaps in a weaker form, suffice for to be a quotient group of G. 
Steinberger, Meir. On Multiplicative Properties of Families of Complexes of Certain Loops. Canadian journal of mathematics, Tome 25 (1973) no. 5, pp. 1066-1077. doi: 10.4153/CJM-1973-114-2
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