Equation 677 Database

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Magma 33db130f89d3…

magma 33db130f89d3
Size
511
Isomorphism class hash
33db130f89d34f3b261f4a968ddaf363bc8ec07829d18fd74f541e5b122cdc02
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
yes
Fiber matrix
symmetric: no · normal: yes · rank: 496 (nullity 15) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-06 14:41:03
Display reorder
506,414,412,411,413,417,415,416,410,509,510,228,505,499,508,501,503,502,500,504,498,170,174,154,162,173,151,157,155,167,395,408,394,378,391,389,379,375,377,399,407,383,382,390,406,376,374,396,398,409,393,380,402,388,386,405,401,171,175,156,158,172,150,163,179,168,166,145,147,176,160,152,153,177,169,146,144,149,159,161,148,164,178,165,397,385,387,381,403,392,384,404,400,454,460,456,458,459,457,507,455,461,223,227,222,224,225,220,229,226,221,186,495,463,476,482,480,485,488,497,490,112,137,114,25,9,120,55,134,118,372,290,268,270,252,249,324,238,293,236,237,348,317,326,362,283,289,242,302,351,235,279,259,261,307,266,337,88,15,45,62,59,71,127,109,98,52,27,24,126,70,58,103,0,94,32,2,68,5,8,101,16,28,140,357,308,277,262,255,285,355,369,352,445,439,442,435,427,436,426,440,452,203,208,202,214,215,218,187,209,219,197,466,470,464,471,491,478,493,468,492,93,57,142,47,29,119,117,54,18,367,298,295,251,244,257,311,280,364,341,232,328,299,304,334,330,276,286,263,248,253,233,338,231,360,321,272,81,64,123,105,89,44,87,61,14,26,108,77,84,41,67,74,1,92,130,20,46,12,3,13,33,36,133,274,241,267,358,291,309,371,316,342,447,424,450,431,446,434,443,449,437,212,210,213,206,207,217,196,211,216,192,474,467,472,477,465,489,473,486,484,37,96,106,75,82,121,135,141,56,356,256,250,312,243,281,282,230,292,353,343,339,370,322,296,365,246,361,300,305,335,331,313,347,325,346,318,128,99,72,110,50,78,85,42,38,124,11,131,34,65,138,90,95,113,30,143,22,21,49,48,6,10,115,315,373,287,303,333,329,350,344,264,432,438,420,444,433,423,430,448,421,189,190,188,201,200,182,193,191,183,198,462,479,469,475,487,481,483,496,494,7,19,63,104,80,122,17,116,136,314,269,254,284,278,271,294,239,297,240,366,323,340,327,363,234,345,319,306,265,336,301,245,310,260,258,288,83,107,40,76,4,39,86,125,43,60,97,111,129,73,91,66,132,139,35,79,102,100,51,69,23,31,53,368,354,273,359,332,349,320,275,247,451,419,429,428,441,422,418,425,453,194,180,195,204,205,184,199,181,185 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 511 = 11 + 5*100, from a common submagma at infinity. C(E, M, k, B) adjoins a submagma M (m elements) of a model E to every group of a transversal design TD(k, g), g = |E| - m, so that every enlarged group is a copy of E and all of them share M; every block carries B, a model of order k in which x*x = x. Two elements of M multiply in M; an element of M or of group i with one of group i, in group i's copy of E; elements of different groups, in their block. It satisfies Equation 677 whenever E and B do. This magma is C(E, M, 5, B) with E = P(11, 6, magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc, 0), M = {1, 11, 21, 31, 41, 51, 61, 71, 81, 91, 101} in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. Labels: 0..m-1 are M, in increasing order of their labels in E; m + g*i + c (i < k, c < g) is point c of group i, which plays the c-th element of E outside M, in increasing order. A block's point in group i plays element i of B. TD(5, 100): MacNeish's product over GF(4) x GF(25); GF(4) = F_2[x]/(x^2 + x + 1), GF(25) = F_5[x]/(x^2 + 2); GF(p^r) = F_p[x]/(f) labels c_0 + c_1 x + ... as c_0 + c_1 p + ..., and point c of a group is the c-th element of the product in lexicographic order. Block (a, b), a and b in the product, meets group i in the point whose coordinate in each field is a + s_i b, s_i the element of that field labelled i, or b when the field has exactly i elements. P(l, q, S, v) is the Paley pencil over Z/l with multiplier q on the seed S of order K + 1 with vertex v: S is relabelled with v as 0 and its other elements as 1..K in increasing order; the points are 0 (the vertex) and 1 + K x + t for (x, t) in Z/l x Z/K; points of one line, or a point and the vertex, multiply as in S (0 the vertex, t + 1 the point (x, t)); and (x, s)*(y, t) for x != y is ((1-q)x + qy, t) when y - x is a nonzero square mod l, else ((1-q)x + qy, -s-t mod K). Equation 255: satisfied. Idempotent elements: 511.

last edited by qawbecrdtey at 2026-10-06 14:41:04 · history