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Embedding Methods for Periodic Groups
Author(s) -
Phillips Richard E.
Publication year - 1979
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-38.1.152-s
Subject(s) - lemma (botany) , mathematics , mathematical proof , embedding , statement (logic) , set (abstract data type) , combinatorics , group (periodic table) , discrete mathematics , computer science , law , physics , ecology , geometry , poaceae , quantum mechanics , artificial intelligence , political science , biology , programming language
The proof of Lemma 3, p. 244, is incorrect. The statement w −1 ɛ Tt 1 −1 ∩ Tt 2 −1 ∩ Tt 3 −1 should read w −1 ɛ t 1 −1 T ∩ t 2 −1 T ∩ t 3 −1 T . Also, it can be shown that Lemma 3, as stated, is false. Fortunately, the situation can be remedied by changing the definition of an S 2 ‐subset (on p. 242) to read A subset T of a group G is of type S 2 if for each set { x , y , z } of three distinct elements of T , Tx −1 ∩ Ty −1 ∩ Tz −1 = x −1 T ∩ y −1 T ∩ z −1 T = {1}. Using this definition, we can see that Lemma 3 is true as stated, while the important Lemma 2 also remains true. All subsequent statements regarding S 2 ‐subsets stand as in the paper, and consequently, the main theorems and their proofs are correct as stated.