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Factorization numbers of finite abelian groups | ||
| International Journal of Group Theory | ||
| مقاله 1، دوره 2، شماره 2، شهریور 2013، صفحه 1-8 اصل مقاله (427.84 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2013.1599 | ||
| نویسنده | ||
| Mohammad Farrokhi Derakhshandeh Ghouchan* | ||
| Ferdowsi University of Mashhad | ||
| چکیده | ||
| The number of factorizations of a finite abelian group as the product of two subgroups is computed in two different ways and a combinatorial identity involving Gaussian binomial coefficients is presented. | ||
| کلیدواژهها | ||
| Factorization number؛ Abelian group؛ subgroup؛ Gaussian binomial coefficient | ||
| مراجع | ||
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G. E. Andrews and K. Eriksson (2004) Integer Partitions Cambridge University Press, Cambridge
W. N. Bailey (1941) A note on certain $q$-identities Quart. J. Math. 12, 173-175
J. N. S. Bidwell and M. J. Curran (2010) Automorphisms of finite Abelian groups Math. Proc. R. Ir. Acad. 110A (1), 57-71
H. Cohn (2004) Projective geometry over $\mathbb{F}_1$ and the Gaussian binomial coefficients Amer. Math. Monthly 111, 487-495
I. J. Davies (1962) Enumeration of certain subgroups of abelian $p$-groups Proc. Edinb. Math. Soc. (2) 13, 1-4
S. Delsarte (1948) Fonctions de Mobius sur les groupes Abeliens finis Ann. of Math. (2) 49, 600-609
M. Golasi\'{n}ski and D. L. Gon\c{c}alves (2008) On automorphisms of finite Abelian $p$-groups Math. Slovaca 58 (4), 405-412
C. J. Hillar and D. L. Rhea (2007) Automorphisms of finite abelian groups Amer. Math. Monthly 11, 17-23
N. J. S. Hughes (1951) The structure and order of the group of central automorphisms of a finite group Proc. London Math. Soc. 52 (2), 377-385
F. H. Jackson (1941) Certain $q$-identities Quart. J. Math. 12, 167-172
Y. Kinosita (1949) On an enumeration of certain subgroups of a $p$-group J. Osaka Inst. Sci. Tech., Part I 1, 13-20
J. Konvalina (1998) Generalized binomial coefficients and the subset-subspace problem Adv. in Appl. Math. 21, 228-240
M. W. Liebeck, C. E. Praeger and J. Saxl (1990) The maximal factorizations of the finite simple groups and their automorphism groups, iv+151 pp Mem. Amer. Math. Soc. 86 (432)
G. A. Miller (1926) Form of the number of the prime power subgroups of an abelian group Proc. Natl. Acad. Sci. USA 12, 470-472
G. A. Miller (1939) Number of the subgroups of any given abelian group Proc. Natl. Acad. Sci. USA 25, 258-262
G. A. Miller (1939) Independent generators of the subgroups of an abelian group Proc. Natl. Acad. Sci. USA 25, 364-367
F. Saeedi and M. Farrokhi D. G. (2012) Factorization numbers of some finite groups Glasgow J. Math. 54, 345-354
F. Saeedi and M. Farrokhi D. G. Subgroup permutability degree of $PSL(2,p^n)$ to appear in Glasgow J. Math.
P. R. Sanders (1969) The central automorphisms of a finite group J. London Math. Soc. 44, 225-228
K. Shoda (1928) \"{U}ber die Automorphismen einer endlischen Abelschen Gruppe Math. Ann. 100, 674-686
T. Stehling (1992) On computing the number of subgroups of a finite Abelian group Combinatorica 12 (4), 475-479
M. T\v{a}rn\v{a}uceanu (2009) Subgroup commutativity degrees of finite groups J. Algebra 321 (9), 2508-2520
Y. Yeh (1948) On prime power abelian groups Bull. Amer. Math. Soc. 54, 323-327
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