Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma db1bdd96c7ff…

magma db1bdd96c7ff
Size
705
Isomorphism class hash
db1bdd96c7ffe2966e91b86c556aa9cbb04a3e323915df143d928017420551bf
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 704) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-03 17:30:09
Display reorder
660,30,128,67,228,221,31,129,229,219,68,32,130,66,230,220,131,33,70,227,224,132,34,71,225,222,133,35,69,226,223,28,126,65,234,216,29,127,63,235,217,27,125,64,236,218,24,122,61,233,215,25,123,62,231,213,26,124,60,232,214,666,662,661,672,256,345,333,321,399,257,346,322,400,334,255,347,335,323,401,348,259,336,324,402,349,260,337,325,403,350,258,338,326,404,254,351,339,327,397,252,352,340,328,398,253,353,341,329,396,250,354,342,330,393,251,355,343,331,394,249,356,344,332,395,690,686,685,687,169,149,239,471,387,170,150,472,388,237,168,151,238,473,389,148,165,242,474,390,146,166,240,475,391,147,167,241,476,392,175,155,245,469,385,176,156,243,470,386,174,157,244,468,384,171,154,248,465,381,172,152,246,466,382,173,153,247,467,383,667,663,665,668,117,272,435,363,284,118,270,364,282,436,116,271,437,365,283,268,120,438,366,280,269,121,439,367,281,267,119,440,368,279,115,263,433,361,275,113,261,434,362,273,114,262,432,360,274,111,266,429,357,278,112,264,430,358,276,110,265,431,359,277,674,678,673,677,36,423,507,519,296,37,424,520,294,508,38,425,509,521,295,426,39,510,522,292,427,40,511,523,293,428,41,512,524,291,42,421,505,517,287,43,422,506,518,285,44,420,504,516,286,45,417,501,513,290,46,418,502,514,288,47,419,503,515,289,670,671,664,669,19,459,447,495,145,20,460,496,143,448,18,461,449,497,144,462,22,450,498,141,463,23,451,499,142,464,21,452,500,140,17,457,445,493,136,15,458,446,494,134,16,456,444,492,135,13,453,441,489,139,14,454,442,490,137,12,455,443,491,138,696,697,695,694,91,103,164,586,629,92,642,643,640,641,93,644,647,645,646,648,94,651,649,650,652,95,655,653,654,656,96,659,657,658,97,106,162,584,624,98,104,163,585,625,99,105,161,583,623,100,109,158,580,627,101,107,159,581,628,102,108,160,582,626,701,702,703,704,298,605,52,84,561,299,606,630,631,53,297,607,51,633,632,608,301,48,635,634,609,302,49,637,636,610,300,50,639,638,304,603,58,88,567,305,604,59,89,565,303,602,57,90,566,307,599,54,87,563,308,600,55,85,564,306,601,56,86,562,699,700,698,693,210,3,411,593,483,211,4,594,484,412,212,5,413,595,485,2,209,414,596,486,1,207,415,597,487,0,208,416,598,488,201,9,409,591,481,202,10,410,592,482,203,11,408,590,480,204,8,405,587,477,205,6,406,588,478,206,7,407,589,479,682,679,684,676,316,543,574,617,375,317,544,618,376,575,315,545,576,619,377,546,319,577,620,378,547,320,578,621,379,548,318,579,622,380,314,541,572,615,373,312,542,573,616,374,313,540,571,614,372,310,537,568,611,369,311,538,569,612,370,309,539,570,613,371,683,675,680,681,74,198,182,555,531,72,199,556,532,180,73,200,181,557,533,197,77,178,558,534,195,75,179,559,535,196,76,177,560,536,80,189,188,553,529,78,190,186,554,530,79,191,187,552,528,83,192,184,549,525,81,193,185,550,526,82,194,183,551,527,689,688,692,691 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 705 = 1 + 11*64, 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, 11, B) with E = magma#58222ccd0574e7adf03b9b32a848bfc3e464df8d7127a3e76f96a819fe65341a, M = {60} in E, B = magma#ca58a4a9ddeee171fc40b5c556a5095e4a2c63eee13557dcdf190986f06d14c3. 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(11, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + x + 1); 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. Equation 255: satisfied. Idempotent elements: 45.

last edited by qawbecrdtey at 2026-10-03 17:30:10 · history