Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma 1563569bb5ba…

magma 1563569bb5ba
Size
705
Isomorphism class hash
1563569bb5ba52f378fefbe17e55354d9e56646c906a741dab697cad2a582ad0
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 17:35:25
Display reorder
660,545,346,291,3,119,546,347,289,4,120,290,547,5,118,348,544,287,349,2,122,542,288,350,1,123,543,286,351,0,121,352,297,9,536,125,353,295,10,537,126,354,296,11,538,124,293,355,8,539,128,294,356,6,540,129,292,357,7,541,127,669,672,666,671,581,391,65,222,13,582,392,66,220,14,64,583,221,12,393,580,68,390,225,16,578,69,388,223,17,579,67,389,224,15,382,63,217,572,19,383,61,218,573,20,384,62,219,574,18,59,385,216,575,22,60,386,214,576,23,58,387,215,577,21,689,691,687,686,427,463,487,321,511,428,464,488,319,512,489,429,320,513,465,426,486,462,317,510,424,484,460,318,508,425,485,461,316,509,454,478,312,418,502,455,479,310,419,503,456,480,311,420,504,481,457,315,421,505,482,458,313,422,506,483,459,314,423,507,664,667,668,665,232,155,171,74,533,233,156,169,75,534,170,234,73,535,154,235,167,158,70,532,236,168,159,71,530,237,166,157,72,531,161,177,80,230,524,162,175,81,231,525,160,176,79,229,526,173,164,76,226,527,174,165,77,227,528,172,163,78,228,529,673,675,679,677,593,379,189,82,403,594,380,187,83,404,188,595,84,405,381,592,185,378,85,402,590,186,376,86,400,591,184,377,87,401,370,180,88,584,394,371,178,89,585,395,372,179,90,586,396,183,373,91,587,397,181,374,92,588,398,182,375,93,589,399,670,662,663,661,439,367,557,137,309,440,368,558,138,307,559,441,136,308,369,438,556,366,140,305,436,554,364,141,306,437,555,365,139,304,358,548,135,430,300,359,549,133,431,298,360,550,134,432,299,551,361,131,433,303,552,362,132,434,301,553,363,130,435,302,695,698,693,694,24,617,523,38,651,654,655,653,39,652,656,657,37,659,658,27,522,616,34,648,25,520,614,35,649,26,521,615,36,650,608,514,44,30,643,609,515,45,28,644,610,516,43,29,642,517,611,40,33,646,518,612,41,31,647,519,613,42,32,645,701,703,702,704,148,451,627,192,569,149,452,628,190,570,629,150,191,571,453,151,626,450,195,568,152,624,448,193,566,153,625,449,194,567,442,618,198,146,560,443,619,196,147,561,444,620,197,145,562,621,445,201,142,563,622,446,199,143,564,623,447,200,144,565,697,700,699,696,475,284,499,342,106,476,285,500,340,107,501,477,341,108,283,474,498,280,345,109,472,496,281,343,110,473,497,282,344,111,275,490,337,466,112,276,491,338,467,113,274,492,339,468,114,493,278,336,469,115,494,279,334,470,116,495,277,335,471,117,676,678,684,682,639,207,605,48,415,640,205,606,46,416,607,641,47,417,206,638,604,203,51,414,636,602,204,49,412,637,603,202,50,413,213,596,54,630,406,211,597,52,631,407,212,598,53,632,408,599,209,57,633,409,600,210,55,634,410,601,208,56,635,411,683,681,674,680,329,243,252,99,266,330,241,250,97,267,251,328,98,265,242,332,255,239,95,262,333,253,240,96,263,331,254,238,94,264,249,258,105,327,272,247,256,103,325,273,248,257,104,326,271,261,245,101,323,268,259,246,102,324,269,260,244,100,322,270,690,688,692,685 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#59c0dab3d55e83047c113809dcb6925b23956e0c747f2365bb6fbba97ebd5493, 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 17:35:26 · history