TABLE OF CONTENTS

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11.2 Decomposition of an operand; fully reducible operands and

semigroups . . . . . . . .

(Theorem 11.3-Theorem 11.4)

11.3 Strictly cyclic operands and modular right congruences.

(Lemma 11.5-Theorem 11.10)

11.4 Representations by one-to-one partial transformations.

(Corollary 11.11-Corollary 11.15)

11.5 Irreducible and transitive operands and semigroups.

(Lemma 11.16-Theorem 11.22)

11.6 Various radicals of a semigroup . . . . .

(Theorem 11.23-Corollary 11.27)

11.7 The normalizer of a right congruence p and the endomorphisms

of Sip

(Theorem 11.28)

11.8 Representations by monomial matrices

(Theorem 11.29)

11.9 Other types of representations . . . . .

(Lemma 11.30-Lemma 11.32)

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CHAPTER 12. EMBEDDING A SEMIGROUP IN A GROUP

12.1 The free group on a semigroup . . . . .

(Lemma 12.1-Construction 12.3)

12.2 The general problem of embedding a semigroup in a group

(Theorem 12.4-Theorem 12.6)

12.3 Ptak's conditions for embeddability .

(Theorem 12.7-Theorem 12.10)

12.4 The construction of quotients . . . .

(Lemma 12.11-Lemma 12.15)

12.5 Lambek's polyhedral conditions for embeddability

(Theorem 12.16)

12.6 Malcev's conditions for embeddability

(Theorem 12.17-Lemma 12.20)

12.7 Comparison of Malcev and Lambek systems

(Theorem 12.21-Lemma 12.23)

12.8 Finite sets of equational implications .

(Lemma 12.24-Corollary 12.31)

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BIBLIOGRAPHY

ERRATA TO VOLUME I

AUTHOR INDEX .

INDEX

APPENDIX .

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