An Outer Commutator Multiplier and Capability of Finitely Generated Abelian Groups

REFERENCES

• Baer , R. ( 1938 ). Groups with preassigned central and central quotient group . Trans. Amer. Math. Soc. 44 : 387 – 412 .
   Google Scholar
• Baer , R. ( 1945 ). Representations of groups as quotient groups I, II, III . Trans. Amer. Math. Soc. 58 : 295 – 419 .
   Web of Science ®Google Scholar
• Beyl , F. R. , Felgner , U. , Schmid , P. ( 1979 ). On groups occuring as center factor groups . J. Algebra 61 : 161 – 177 .
   Web of Science ®Google Scholar
• Burns , J. , Ellis , G. ( 1997 ). On the nilpotent multipliers of a group . Math. Z. 226 : 405 – 428 .
   Web of Science ®Google Scholar
• Ellis , G. ( 1996 ). Capability, homology, and central series of a pair of groups . J. Algebra 179 : 31 – 46 .
   Web of Science ®Google Scholar
• Fuchs , L. (1970). Infinite Abelian Groups . New York and London : Academic Press.
   Google Scholar
• Hall , M. ( 1959 ). The Theory of Groups . New York : MacMillan Company .
   Google Scholar
• Hall , M. Jr. , Senior , J. K. ( 1964 ). The Groups of Order 2 ⁿ (n ≤ 6) . New York : MacMillan .
   Google Scholar
• Hulse , J. A. , Lennox , J. C. ( 1976 ). Marginal series in groups . Proc. Royal Soc. Edinburgh 76A : 139 – 154 .
   Google Scholar
• Leedham-Green , C. R. , McKay , S. ( 1976 ). Baer-invariant, isologism, varietal laws and homology . Acta Math. 137 : 99 – 150 .
   Web of Science ®Google Scholar
• Magidin , A. ( 2005 ) Capability of nilpotent products of cyclic groups . J. Group Theory 8 ( 4 ): 431 – 452 .
   Web of Science ®Google Scholar
• Mashayekhy , B. , Moghaddam , M. R. R. ( 1997 ). Higher Schur-multiplicator of a finite abelian group . Algebra Colloquium 4 ( 3 ): 317 – 322 .
   Web of Science ®Google Scholar
• Mashayekhy , B. , Parvizi , M. ( 2006 ). Polynilpotent multipliers of finitely generated abelian groups . J. Math. Game Theory Algebra 16 : 93 – 102 .
   Google Scholar
• Moghaddam , M. R. R. , Kayvanfar , S. ( 1997 ). A new notion derived from varieties of groups . Algebra Colloquium 4 ( 1 ): 1 – 11 .
   Web of Science ®Google Scholar
• Parvizi , M. , Mashayekhy , B. , and Kayvanfar , S. Polynilpotent capability of finitely generated abelian groups . Submitted .
   Google Scholar
• Schur , I. ( 1907 ). Untersuchungen über die darstellung der endlichen gruppen durch gebrochene lineare substitutionen . J. Reine Angew. Math. 132 : 85 – 137 .
   Google Scholar
• Stroud , P. W. ( 1965 ). On a property of verbal and marginal subgroups . Proc. Cambridge Phil. Soc. 61 : 41 – 48 .
   Web of Science ®Google Scholar
• Teague , T. K. ( 1974 ). On the Engel margin . Pacific Journal of Mathematics 50 ( 1 ): 205 – 214 .
   Web of Science ®Google Scholar
• Communicated by A. Olshanskii.
   Google Scholar