Notes on Frattini Subgroups of Generalized Free Products with Cyclic Amalgamation
Canadian mathematical bulletin, Tome 23 (1980) no. 1, pp. 51-59
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The problem of the exact location of the Frattini subgroup 4>(G) of a generalized free product G = (A*B)H was first raised by Higman and Neumann [5]. Solutions to special cases of the problem can be found in [1], [2], [8], [9] and [10]. The purpose of this note is to extend the results of [2], [8], and to simplify the proof of Whittemore's theorem [10]. We also apply our result to give simple proofs of certain classes of knot groups that have trivial Frattini subgroups. The proof that every knot group has trivial Frattini subgroup hard and long (footnote 2, p. 56).
Allenby, R. B. J. T.; Tang, C. Y.; Tang, S. Y. Notes on Frattini Subgroups of Generalized Free Products with Cyclic Amalgamation. Canadian mathematical bulletin, Tome 23 (1980) no. 1, pp. 51-59. doi: 10.4153/CMB-1980-007-0
@article{10_4153_CMB_1980_007_0,
author = {Allenby, R. B. J. T. and Tang, C. Y. and Tang, S. Y.},
title = {Notes on {Frattini} {Subgroups} of {Generalized} {Free} {Products} with {Cyclic} {Amalgamation}},
journal = {Canadian mathematical bulletin},
pages = {51--59},
year = {1980},
volume = {23},
number = {1},
doi = {10.4153/CMB-1980-007-0},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1980-007-0/}
}
TY - JOUR AU - Allenby, R. B. J. T. AU - Tang, C. Y. AU - Tang, S. Y. TI - Notes on Frattini Subgroups of Generalized Free Products with Cyclic Amalgamation JO - Canadian mathematical bulletin PY - 1980 SP - 51 EP - 59 VL - 23 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1980-007-0/ DO - 10.4153/CMB-1980-007-0 ID - 10_4153_CMB_1980_007_0 ER -
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