Equation 677 Database

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Magma d6f29cd18797…

magma d6f29cd18797
Size
705
Isomorphism class hash
d6f29cd18797c95a94742338a98bc43fceb07fd4a1c3aac1c8a82556f457cd3b
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 19:48:54
Display reorder
660,289,550,352,321,424,287,548,350,322,422,288,549,351,320,423,285,553,355,324,427,286,551,353,325,425,284,552,354,323,426,545,295,347,327,419,546,293,348,328,420,294,547,349,326,421,291,544,346,330,418,292,542,344,331,416,290,543,345,329,417,688,675,677,674,60,376,76,514,30,61,374,74,512,31,59,375,75,513,29,56,379,79,517,26,57,377,77,515,27,58,378,78,516,28,371,51,82,509,36,372,52,80,510,37,50,373,81,511,35,54,370,85,508,32,55,368,83,506,33,53,369,84,507,34,662,672,668,669,10,488,340,526,464,8,486,338,524,462,9,487,339,525,463,13,491,343,529,467,11,489,341,527,465,12,490,342,528,466,483,23,335,521,459,484,24,336,522,460,21,485,337,523,461,15,482,334,520,458,16,480,332,518,456,18,481,333,519,457,683,673,681,686,127,632,630,634,628,125,616,614,618,612,126,624,622,626,620,123,656,654,658,652,124,640,638,642,636,122,648,646,650,644,592,133,590,594,588,600,131,598,602,597,132,608,606,610,605,129,583,581,585,584,130,452,7,504,147,128,453,6,505,146,697,700,703,704,105,173,388,400,297,106,171,386,398,298,104,172,387,399,296,108,169,391,403,300,109,170,389,401,301,107,168,390,402,299,164,103,383,395,303,162,101,384,396,304,102,163,385,397,302,99,167,382,394,306,100,165,380,392,307,98,166,381,393,305,689,690,693,691,445,216,40,113,22,443,217,38,114,25,444,218,39,115,20,441,219,43,112,14,442,220,41,110,17,440,221,42,111,19,214,451,46,119,4,215,449,44,120,5,450,213,45,121,3,447,210,49,118,1,448,211,47,116,0,446,212,48,117,2,670,664,661,665,252,573,572,261,187,253,568,569,262,188,254,571,570,263,186,255,579,578,260,190,256,574,575,258,191,257,577,576,259,189,562,250,563,267,193,564,251,565,268,194,249,567,566,269,192,246,561,560,266,196,247,556,557,264,197,248,559,558,265,195,696,695,692,694,137,500,436,538,209,138,498,434,536,207,139,499,435,537,208,136,503,439,541,205,134,501,437,539,206,135,502,438,540,204,495,143,431,533,200,496,144,432,534,198,145,497,433,535,199,142,494,430,532,203,140,492,428,530,201,141,493,429,531,202,684,678,682,687,280,633,635,631,629,281,617,619,615,613,279,625,627,623,621,276,657,659,655,653,277,641,643,639,637,278,649,651,647,645,593,271,595,591,589,601,272,603,599,596,270,609,611,607,604,274,586,587,582,580,275,455,554,283,148,273,454,555,282,149,699,702,701,698,72,412,157,476,96,73,410,158,474,97,71,411,156,475,95,68,415,160,479,92,69,413,161,477,93,70,414,159,478,94,407,63,155,471,87,408,64,153,472,88,62,409,154,473,86,66,406,151,470,90,67,404,152,468,91,65,405,150,469,89,663,666,671,667,180,364,233,317,244,181,362,231,318,245,182,363,232,319,243,183,367,229,316,240,184,365,230,314,241,185,366,228,315,242,359,178,224,308,235,360,179,222,309,236,177,361,223,310,234,174,358,227,311,238,175,356,225,312,239,176,357,226,313,237,676,680,685,679 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#ad2693ca9f316a407649b357541de7a5de95f31142bb6f4854bfa44084f1f633, M = {60} in E, B = magma#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc. 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 19:48:55 · history