Equation 677 Database

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Magma b1344cc08966…

magma b1344cc08966
Size
705
Isomorphism class hash
b1344cc089665cad948cd1b9ca010da59a5379c5f33d6f64b8df39bd690dbd39
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 18:10:28
Display reorder
660,416,130,117,320,324,414,131,118,318,325,415,129,119,319,326,419,126,323,327,116,417,127,114,321,328,418,128,115,322,329,108,411,315,121,330,109,412,316,122,331,110,413,317,120,332,410,111,314,124,333,408,112,312,125,334,123,409,113,313,335,661,665,666,672,59,94,464,236,614,57,95,462,234,612,58,93,463,235,613,55,90,239,617,467,56,91,465,237,615,54,92,466,238,616,459,50,231,85,609,460,48,232,86,610,461,49,233,84,611,53,458,230,88,608,51,456,228,89,606,87,52,457,229,607,690,689,685,686,584,181,536,356,155,582,182,534,354,153,583,180,535,355,154,587,184,359,151,539,585,185,537,357,152,586,183,538,358,150,531,579,351,187,146,532,580,352,188,144,533,581,353,186,145,578,530,350,190,149,576,528,348,191,147,189,577,529,349,148,663,667,670,669,244,361,602,106,452,245,362,600,107,450,243,360,601,105,451,240,364,102,455,605,241,365,603,103,453,242,363,604,104,454,597,250,97,367,447,598,251,98,368,448,599,249,96,366,449,246,596,100,370,446,247,594,101,371,444,369,248,595,99,445,679,674,675,682,440,202,67,253,380,438,203,68,254,378,439,201,66,252,379,443,198,256,383,70,441,199,71,257,381,442,200,69,255,382,65,435,259,193,375,63,436,260,194,376,64,437,258,192,377,434,61,262,196,374,432,62,263,197,372,195,433,60,261,373,671,664,668,662,428,133,488,572,339,426,134,486,570,340,427,132,487,571,341,431,136,575,338,491,429,137,489,573,336,430,135,490,574,337,483,423,567,139,345,484,424,568,140,346,485,425,569,138,347,422,482,566,142,344,420,480,564,143,342,141,421,481,565,343,697,693,694,695,644,29,647,646,645,638,27,639,637,636,640,28,643,642,641,656,25,658,657,659,649,26,651,650,648,653,24,655,654,652,621,589,46,20,3,622,590,47,18,4,623,588,45,19,5,592,620,42,23,2,593,618,43,21,1,22,591,619,44,0,703,701,702,704,628,206,277,629,512,624,204,278,625,510,626,205,276,627,511,634,209,635,515,280,630,207,281,631,513,632,208,279,633,514,283,269,272,212,507,284,267,270,210,508,282,268,271,211,509,265,286,275,215,506,266,287,273,213,504,214,264,285,274,505,700,696,699,698,500,309,179,405,394,498,310,177,406,395,499,311,178,407,393,503,308,404,390,175,501,306,176,402,391,502,307,174,403,392,170,495,396,300,385,168,496,397,301,386,169,497,398,302,384,494,173,399,303,388,492,171,400,304,389,305,493,172,401,387,678,683,676,680,296,77,524,548,222,294,75,522,546,223,295,76,523,547,224,299,73,551,225,527,297,74,525,549,226,298,72,526,550,227,519,291,543,83,220,520,292,544,81,221,521,293,545,82,219,290,518,542,79,216,288,516,540,80,217,78,289,517,541,218,684,673,681,677,33,164,6,560,476,35,162,7,558,474,30,163,8,559,475,38,167,563,479,9,40,165,10,561,477,36,166,11,562,478,12,37,555,159,471,13,39,556,160,472,14,41,557,161,473,34,15,554,158,470,31,16,552,156,468,157,32,17,553,469,687,692,688,691 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#676093fc8b0a9c703c9b4a913f63a03a075a7ec27635c2c42c5b015ba025ae64, 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 18:10:29 · history