A class of finite groupamalgams
Author:
Dragomir Ž. Djoković
Journal:
Proc. Amer. Math. Soc. 80 (1980), 2226
MSC:
Primary 20E99
MathSciNet review:
574502
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Abstract: Let and be finite groups such that is a common subgroup with and . We further assume that only the trivial subgroup of is normal in both and . Let K be the intersection of all conjugates for . Then if we have , or . We describe in detail all such amalgams when (dihedral group of order 8). There are infinitely many of them, while if or there are only finitely many amalgams.
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Dragomir
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 [1]
 D. Ž. Djoković and G. L. Miller, Regular groups of automorphisms of cubic graphs, J. Combinatorial Theory Ser. B (to appear). MR 538042 (81f:05092)
 [2]
 D. Ž. Djoković, Automorphisms of regular graphs and finite simple groupamalgams (preprint). MR 642035 (83h:05045)
 [3]
 A. Gardiner, Doubly primitive vertex stabilisers in graphs, Math. Z. 135 (1974), 257266. MR 0412014 (54:143)
 [4]
 , Arc transitivity in graphs. II, Quart. J. Math. Oxford Ser. (2) 25 (1974), 163167. MR 0412015 (54:144)
 [5]
 G. Glauberman, Isomorphic subgroups of finite pgroups. I, Canad. J. Math. 23 (1971), 9831022. MR 0374262 (51:10462)
 [6]
 D. M. Goldschmidt, Automorphisms of trivalent graphs (preprint). MR 569075 (82a:05052)
 [7]
 J.P. Serre, Arbres, amalgames, , Astérisque 46 (1977).
 [8]
 C. C. Sims, Graphs and finite permutation groups. II, Math. Z. 103 (1968), 276281. MR 0225865 (37:1456)
 [9]
 W. T. Tutte, Connectivity in graphs, Univ. of Toronto Press, Toronto, 1966. MR 0210617 (35:1503)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939198005745029
PII:
S 00029939(1980)05745029
Article copyright:
© Copyright 1980
American Mathematical Society
