-
1
-
-
33750994100
-
1, isoperimetric inequalities for graphs, and superconcentrators
-
1, isoperimetric inequalities for graphs, and superconcentrators; J. Comb. Theory, Ser. B 38 (1985), 73-88.
-
(1985)
J. Comb. Theory, Ser. B
, vol.38
, pp. 73-88
-
-
Alon, N.1
Milman, V.D.2
-
3
-
-
0001527133
-
The probability of generating the symmetric group
-
L. BABAI: The probability of generating the symmetric group, J. Comb. Th. Ser. A 52 (1989), 148-153.
-
(1989)
J. Comb. Th. Ser. A
, vol.52
, pp. 148-153
-
-
Babai, L.1
-
4
-
-
84976782048
-
Local expansion of vertex-transitive graphs and random generation in finite groups
-
rd ACM STOC, 1991, pp. 164-174.
-
(1991)
rd ACM STOC
, pp. 164-174
-
-
Babai, L.1
-
5
-
-
0001460029
-
Automorphism groups, isomorphism, reconstruction
-
(R. L. Graham, M. Groetschel and L. Lovasz, eds.), Elsevier
-
L. BABAI: Automorphism groups, isomorphism, reconstruction; in: Handbook of Combinatorics (R. L. Graham, M. Groetschel and L. Lovasz, eds.), Elsevier, 1996.
-
(1996)
Handbook of Combinatorics
-
-
Babai, L.1
-
6
-
-
0007076247
-
Randomization in group algorithms: Conceptual questions
-
(L. Finkelstein, W. M. Kantor, eds.), DIMACS Workshops on Groups and Computation, AMS, Providence
-
L. BABAI: Randomization in group algorithms: Conceptual questions, in: Groups and Computation II (L. Finkelstein, W. M. Kantor, eds.), DIMACS Workshops on Groups and Computation, AMS, Providence, 1997.
-
(1997)
Groups and Computation II
-
-
Babai, L.1
-
7
-
-
84971790005
-
On the diameter of random Cayley graphs of the symmetric group
-
L. BABAI and G. L. HETYEI: On the diameter of random Cayley graphs of the symmetric group, Combin. Probab. Comput. 1 (1992), 201-208.
-
(1992)
Combin. Probab. Comput.
, vol.1
, pp. 201-208
-
-
Babai, L.1
Hetyei, G.L.2
-
9
-
-
85009806236
-
Small-diameter Cayley graphs for finite simple groups
-
L. BABAI, W. M. KANTOR and A. LUBOTZKY: Small-diameter Cayley graphs for finite simple groups, European J. Combin. 10 (1989), 507-522.
-
(1989)
European J. Combin.
, vol.10
, pp. 507-522
-
-
Babai, L.1
Kantor, W.M.2
Lubotzky, A.3
-
12
-
-
21844515117
-
Generating random elements of a finite group
-
F. CELLER, C. R. LEEDHAM-GREEN, S. MURRAY, A. NIEMEYER and E. A. O'BRIEN: Generating random elements of a finite group, Comm. Algebra 23 (1995), 4931-4948.
-
(1995)
Comm. Algebra
, vol.23
, pp. 4931-4948
-
-
Celler, F.1
Leedham-Green, C.R.2
Murray, S.3
Niemeyer, A.4
O'Brien, E.A.5
-
14
-
-
0008242702
-
Random walks on generating sets for finite groups
-
F. R. K. CHUNG and R. L. GRAHAM: Random walks on generating sets for finite groups, Electronic J. of Comb. 4:2 (1997), #R7.
-
(1997)
Electronic J. of Comb.
, vol.4
, Issue.2
-
-
Chung, F.R.K.1
Graham, R.L.2
-
15
-
-
0032400054
-
Isoperimetric inequalities for cartesian products of graphs
-
F. R. K. CHUNG and P. TETALI: Isoperimetric inequalities for cartesian products of graphs, Combin. Probab. Comput 7 (1998), 141-148.
-
(1998)
Combin. Probab. Comput
, vol.7
, pp. 141-148
-
-
Chung, F.R.K.1
Tetali, P.2
-
16
-
-
21344463814
-
A group theoretic criterion for property FA
-
M. CULLER and K. VOGTMANN: A group theoretic criterion for property FA, Proc. Amer. Math. Soc. 124 (1996), 677-683.
-
(1996)
Proc. Amer. Math. Soc.
, vol.124
, pp. 677-683
-
-
Culler, M.1
Vogtmann, K.2
-
17
-
-
0012526216
-
-
Cambridge University Press, Cambridge
-
G. DAVIDOFF, P. SARNAK and A. VALETTE: Elementary number theory, group theory, and Ramanujan graphs; Cambridge University Press, Cambridge, 2003.
-
(2003)
Elementary Number Theory, Group Theory, and Ramanujan Graphs
-
-
Davidoff, G.1
Sarnak, P.2
Valette, A.3
-
19
-
-
0001076208
-
Comarison techniques for random walk on finite groups
-
P. DIACONIS and L. SALOFF-COSTE: Comarison techniques for random walk on finite groups, Annals of Probability 21 (1993), 2131-2156.
-
(1993)
Annals of Probability
, vol.21
, pp. 2131-2156
-
-
Diaconis, P.1
Saloff-Coste, L.2
-
21
-
-
0040676602
-
Walks on generating sets of groups
-
P. DIACONIS and L. SALOFF-COSTE: Walks on generating sets of groups, Invent. Math. 134 (1998), 251-199.
-
(1998)
Invent. Math.
, vol.134
, pp. 251-1199
-
-
Diaconis, P.1
Saloff-Coste, L.2
-
22
-
-
0000660463
-
The probability of generating the symmetric group
-
J. D. DIXON: The probability of generating the symmetric group, Math. Z. 110 (1969), 199-205.
-
(1969)
Math. Z.
, vol.110
, pp. 199-205
-
-
Dixon, J.D.1
-
24
-
-
0142168845
-
Spectral gap for infinite index "congruence" subgroups
-
A. GAMBURD: Spectral gap for infinite index "congruence" subgroups, Israel Journal of Mathematics 127 (2002), 157-200.
-
(2002)
Israel Journal of Mathematics
, vol.127
, pp. 157-200
-
-
Gamburd, A.1
-
26
-
-
0001615330
-
Finite quotients of the automorphism group of a free group
-
R. GILMAN: Finite quotients of the automorphism group of a free group, Canad. J. Math. 29 (1977), 541-551.
-
(1977)
Canad. J. Math.
, vol.29
, pp. 541-551
-
-
Gilman, R.1
-
27
-
-
0039299629
-
-
Math. Sci. Res. Inst. Publ., 8, Springer, New York
-
M. GROMOV: Hyperbolic groups, Math. Sci. Res. Inst. Publ., 8, Springer, New York, 1987.
-
(1987)
Hyperbolic Groups
-
-
Gromov, M.1
-
30
-
-
77955478020
-
The Eulerian functions of a group
-
P. HALL: The Eulerian functions of a group, Quart. J. Math. 7 (1936), 134-151.
-
(1936)
Quart. J. Math.
, vol.7
, pp. 134-151
-
-
Hall, P.1
-
32
-
-
0024904712
-
Approximating the permanent
-
M. JERRUM, A. SINCLAIR: Approximating the permanent, SIAM J. Comput. 18 (1989), 1149-1178.
-
(1989)
SIAM J. Comput.
, vol.18
, pp. 1149-1178
-
-
Jerrum, M.1
Sinclair, A.2
-
33
-
-
0003206125
-
Some topics in asymptotic group theory
-
(Durham, 1990), Cambridge Univ. Press, Cambridge
-
W. M. KANTOR: Some topics in asymptotic group theory, in: Groups, Combinatorics & Geometry (Durham, 1990), Cambridge Univ. Press, Cambridge, 1992, pp. 403-421.
-
(1992)
Groups, Combinatorics & Geometry
, pp. 403-421
-
-
Kantor, W.M.1
-
34
-
-
0007031051
-
Simple groups in computational group theory
-
W. M. KANTOR: Simple groups in computational group theory, in Proc. ICM Berlin, Vol. II (1998), pp. 77-86.
-
(1998)
Proc. ICM Berlin
, vol.2
, pp. 77-86
-
-
Kantor, W.M.1
-
35
-
-
0001941330
-
The probability of generating a finite classical group
-
W. M. KANTOR, A. LUBOTZKY: The probability of generating a finite classical group, Geom. Dedicata 36 (1990), 67-87.
-
(1990)
Geom. Dedicata
, vol.36
, pp. 67-87
-
-
Kantor, W.M.1
Lubotzky, A.2
-
36
-
-
84950854506
-
2 over a finite field and related numerical experiments
-
2 over a finite field and related numerical experiments, Experimental Mathematics 1 (1992), 115-139.
-
(1992)
Experimental Mathematics
, vol.1
, pp. 115-139
-
-
Lafferty, J.1
Rockmore, D.2
-
38
-
-
33749365163
-
-
personal communication
-
C. R. LEEDHAM-GREEN: personal communication.
-
-
-
Leedham-Green, C.R.1
-
39
-
-
0001056702
-
The probability of generating a finite simple group
-
M. W. LIEBECK and A. SHALEV: The probability of generating a finite simple group, Geom. Dedicata 56 (1995), 103-113.
-
(1995)
Geom. Dedicata
, vol.56
, pp. 103-113
-
-
Liebeck, M.W.1
Shalev, A.2
-
40
-
-
0030586644
-
Simple groups, probabilistic methods, and a conjecture of Kantor and Lubotzky
-
M. W. LIEBECK and A. SHALEV: Simple groups, probabilistic methods, and a conjecture of Kantor and Lubotzky; J. Algebra 184 (1996), 31-57.
-
(1996)
J. Algebra
, vol.184
, pp. 31-57
-
-
Liebeck, M.W.1
Shalev, A.2
-
42
-
-
0005856858
-
The product replacement algorithm and Kazhdan's property (T)
-
A. LUBOTZKY and I. PAK: The product replacement algorithm and Kazhdan's property (T), Journal of AMS 52 (2000), 5525-5561.
-
(2000)
Journal of AMS
, vol.52
, pp. 5525-5561
-
-
Lubotzky, A.1
Pak, I.2
-
44
-
-
0037906726
-
Groups and expanders
-
(Princeton, NJ), DIMACS Ser. 10, AMS, Providence, RI
-
A. LUBOTZKY and B. WEISS: Groups and expanders, in: Expanding graphs (Princeton, NJ, 1992), pp. 95-109, DIMACS Ser. 10, AMS, Providence, RI, 1993.
-
(1992)
Expanding Graphs
, pp. 95-109
-
-
Lubotzky, A.1
Weiss, B.2
-
45
-
-
0003430207
-
-
Dover, New York
-
W. MAGNUS, A. KARRASS and D. SOLITAR: Combinatorial group theory, Presentations of groups in terms of generators and relations; Second edition, Dover, New York, 1976.
-
(1976)
Combinatorial Group Theory, Presentations of Groups in Terms of Generators and Relations; Second Edition
-
-
Magnus, W.1
Karrass, A.2
Solitar, D.3
-
47
-
-
0024045909
-
Explicit group theoretic constructions of combinatorial schemes, and their applications for construction of expanders and concentrators
-
G. A. MARGULIS: Explicit group theoretic constructions of combinatorial schemes, and their applications for construction of expanders and concentrators; Problems of Information Transmission 24 (1988), 39-46.
-
(1988)
Problems of Information Transmission
, vol.24
, pp. 39-46
-
-
Margulis, G.A.1
-
49
-
-
33749314812
-
-
personal communication
-
A. ODLYZKO: personal communication.
-
-
-
Odlyzko, A.1
-
50
-
-
0005981336
-
Random walks on finite groups with few random generators
-
I. PAK: Random walks on finite groups with few random generators, Electr. J. Prob. 4 (1999), pp. 1-11.
-
(1999)
Electr. J. Prob.
, vol.4
, pp. 1-11
-
-
Pak, I.1
-
52
-
-
0005896151
-
What do we know about the product replacement algorithm?
-
(W. Kantor, A. Seress, eds.), Berlin
-
I. PAK: What do we know about the product replacement algorithm?, in: Groups and Computation III (W. Kantor, A. Seress, eds.), Berlin, 2000, pp. 301-347.
-
(2000)
Groups and Computation III
, pp. 301-347
-
-
Pak, I.1
-
53
-
-
33749324701
-
The product replacement algorithm is polynomial
-
st IEEE FOCS, 2000.
-
(2000)
st IEEE FOCS
-
-
Pak, I.1
-
54
-
-
0347276616
-
On sampling generating sets of finite groups and the product replacement algorithm
-
th ISSAC, 1999, pp. 91-96.
-
(1999)
th ISSAC
, pp. 91-96
-
-
Pak, I.1
Bratus, S.2
-
55
-
-
0036041153
-
On Kazhdan constants and mixing of random walks
-
I. PAK and A. ZUK: On Kazhdan constants and mixing of random walks, Int. Math. Res. Not. 36 (2002), 1891-1905.
-
(2002)
Int. Math. Res. Not.
, vol.36
, pp. 1891-1905
-
-
Pak, I.1
Zuk, A.2
-
56
-
-
33749319020
-
-
unpublished manuscript
-
J.-J. QUISQUATER: unpublished manuscript.
-
-
-
Quisquater, J.-J.1
-
58
-
-
0040056171
-
Expanding graphs and invariant means
-
Y. SHALOM: Expanding graphs and invariant means, Combinatorica 17 (1997), 555-575.
-
(1997)
Combinatorica
, vol.17
, pp. 555-575
-
-
Shalom, Y.1
-
59
-
-
0142214312
-
Expander graphs and amenable quotients
-
IMA Vol. Math. Appl., Springer, New York
-
Y. SHALOM: Expander graphs and amenable quotients, in: Emerging applications of number theory, pp. 571-581, IMA Vol. Math. Appl., 109, Springer, New York, 1999.
-
(1999)
Emerging Applications of Number Theory
, vol.109
, pp. 571-581
-
-
Shalom, Y.1
-
60
-
-
0000805768
-
Bounded generation and Kazhdan's property (T)
-
Y. SHALOM: Bounded generation and Kazhdan's property (T), Publ. Math. IHES 90 (1999), 145-168.
-
(1999)
Publ. Math. IHES
, vol.90
, pp. 145-168
-
-
Shalom, Y.1
-
61
-
-
21744461823
-
Bounded generation does not imply finite presentation
-
B. SURY: Bounded generation does not imply finite presentation, Comm. Algebra 25 (1997), 1673-1683.
-
(1997)
Comm. Algebra
, vol.25
, pp. 1673-1683
-
-
Sury, B.1
-
62
-
-
0034288629
-
Maximal independent generating sets of the symmetric group
-
J. WHISTON: Maximal independent generating sets of the symmetric group, J. Algebra 232 (2000), 255-268.
-
(2000)
J. Algebra
, vol.232
, pp. 255-268
-
-
Whiston, J.1
-
63
-
-
33749333274
-
-
Ph.D. Thesis, Cambridge University
-
J. WHISTON: Ph.D. Thesis, Cambridge University, 2001.
-
(2001)
-
-
Whiston, J.1
|