Geodesic
A Remark on the Group Rings of Order Preserving Permutation Groups
Canadian mathematical bulletin, Tome 11 (1968) no. 5, pp. 679-680

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If G and H are two groups such that their integral group rings Z(G) and Z(H) are isomorphic, does it follow that G and H are isomorphic? This is the isomorphism problem and an affirmative answer is obtained in case G is a sub group of the group of order preserving permutations of a totally ordered set. 
LaGrange, R.H.; Rhemtulla, A.H. A Remark on the Group Rings of Order Preserving Permutation Groups. Canadian mathematical bulletin, Tome 11 (1968) no. 5, pp. 679-680. doi: 10.4153/CMB-1968-081-9
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     author = {LaGrange, R.H. and Rhemtulla, A.H.},
     title = {A {Remark} on the {Group} {Rings} of {Order} {Preserving} {Permutation} {Groups}},
     journal = {Canadian mathematical bulletin},
     pages = {679--680},
     year = {1968},
     volume = {11},
     number = {5},
     doi = {10.4153/CMB-1968-081-9},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1968-081-9/}
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