Equation 677 Database

← all  ·  ← by size  ·  ← size 511

Magma af891dd02374…

magma af891dd02374
Size
511
Isomorphism class hash
af891dd02374da27824b77342cf2238ba721b0073d97551bb3f51cca4bf2f08e
Satisfies Equation 255
yes
Right-cancellative
no
Idempotent
yes
Fiber matrix
symmetric: no · normal: no · rank: 460 (nullity 51) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-06 19:07:52
Display reorder
472,507,462,449,408,400,402,437,461,469,435,502,498,495,494,493,492,496,497,499,491,501,417,453,429,414,454,440,423,466,465,510,476,478,474,473,480,481,479,475,477,506,427,470,456,438,421,412,433,451,415,509,416,450,434,411,422,439,457,471,428,504,405,446,419,409,431,445,458,442,425,508,404,468,460,436,403,401,407,448,463,500,464,467,424,441,455,413,430,452,418,505,426,443,459,444,432,410,420,447,406,503,482,490,488,487,483,484,485,486,489,256,213,261,367,194,298,296,293,290,300,100,90,96,87,389,67,63,59,56,71,333,328,347,342,338,190,258,184,263,271,316,320,325,306,311,280,286,277,374,273,227,231,233,219,223,362,351,353,356,359,0,8,72,32,382,105,121,168,114,110,16,24,12,20,380,57,54,68,64,60,145,143,140,137,394,5,172,84,177,34,304,309,314,377,323,208,196,204,267,200,53,39,43,47,383,155,160,165,179,151,289,276,279,373,285,255,183,212,193,260,66,55,62,70,386,116,102,112,118,107,332,341,327,337,346,210,266,198,202,206,187,364,268,216,272,234,228,220,368,224,303,318,308,322,313,354,365,357,352,360,93,95,99,86,388,9,79,76,81,3,44,36,48,40,384,130,124,132,127,135,167,157,148,162,396,18,22,26,174,14,182,214,189,366,254,238,245,235,241,249,104,113,120,109,397,144,136,142,176,139,299,294,301,375,291,247,240,251,243,236,75,78,10,29,381,101,97,94,91,88,334,348,339,329,343,292,363,295,376,297,239,250,242,370,246,181,253,211,188,215,199,195,180,207,203,345,336,326,378,331,122,128,133,125,393,51,41,49,37,45,6,82,35,175,398,27,23,19,15,80,153,163,149,158,399,129,134,126,131,123,225,232,221,229,217,191,185,269,259,264,92,89,85,98,390,166,152,161,147,156,248,252,237,371,244,288,282,275,284,278,117,119,103,108,391,74,11,2,77,30,335,340,344,349,330,226,222,218,369,230,281,274,283,372,287,315,310,305,324,319,192,270,262,186,257,361,358,355,379,350,58,61,65,69,385,17,171,21,13,25,106,111,115,178,392,1,28,31,73,7,146,173,138,141,395,52,50,46,42,38,209,201,265,205,197,302,321,317,312,307,4,33,169,83,387,154,150,170,164,159 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, 2, magma#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3, 0), M = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10} 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 19:07:53 · history