Equation 677 Database

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Magma 3c22078536dd…

magma 3c22078536dd
Size
705
Isomorphism class hash
3c22078536ddff3bb13a8cab0c818021649dbe3c9c3e2099382c431f310bb271
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 19:20:39
Display reorder
660,575,246,4,439,499,576,247,440,5,500,441,245,577,3,501,249,574,1,438,498,250,572,0,436,496,248,573,2,437,497,581,244,24,445,505,582,242,25,446,506,583,243,26,447,507,580,240,34,444,504,578,241,27,442,502,579,239,30,443,503,678,677,685,684,156,54,427,357,403,154,55,355,428,404,356,56,155,429,405,57,159,426,353,402,58,157,424,354,400,59,158,425,352,401,151,52,433,363,409,152,53,434,361,410,153,51,435,362,411,150,48,432,359,408,148,49,430,360,406,149,50,431,358,407,663,667,664,661,415,112,379,367,519,416,110,368,380,520,369,111,417,381,521,115,414,378,366,518,113,412,376,364,516,114,413,377,365,517,421,107,385,373,525,422,108,386,374,526,423,109,387,375,527,420,106,384,372,524,418,104,382,370,522,419,105,383,371,523,679,673,675,676,511,98,178,77,142,512,99,78,176,140,79,100,513,177,141,101,510,174,76,145,102,508,175,74,143,103,509,173,75,144,641,96,640,636,637,649,97,648,645,644,657,95,656,653,652,630,92,629,632,633,514,93,339,72,146,515,94,172,73,147,703,698,704,697,587,252,487,451,193,588,253,452,488,191,453,251,589,489,192,255,586,486,450,196,256,584,484,448,194,254,585,485,449,195,593,258,493,457,199,594,259,494,458,197,595,257,495,459,198,592,261,492,456,202,590,262,490,454,200,591,260,491,455,201,693,690,691,694,463,87,170,133,126,464,88,131,171,127,132,86,465,169,125,90,462,166,129,122,91,460,167,130,123,89,461,168,128,124,469,85,161,139,117,470,83,162,137,118,471,84,160,138,116,468,81,164,135,120,466,82,165,136,121,467,80,163,134,119,670,662,672,666,310,221,321,289,279,308,222,287,322,280,288,223,309,320,278,224,306,317,292,275,225,307,318,290,276,226,305,319,291,277,301,219,312,295,285,299,220,313,293,286,300,218,311,294,284,304,215,315,298,281,302,216,316,296,282,303,217,314,297,283,695,689,696,692,13,236,18,619,543,14,237,620,19,544,621,238,12,20,545,235,16,21,618,542,233,17,22,616,540,234,15,23,617,541,11,227,33,625,549,9,228,29,626,550,10,229,31,627,551,7,230,35,624,548,8,231,28,622,546,6,232,32,623,547,681,688,683,674,326,46,611,555,333,327,47,556,612,331,557,45,325,613,332,42,329,610,554,336,43,330,608,552,334,44,328,609,553,335,638,37,643,642,639,646,38,651,650,647,654,36,659,658,655,634,40,635,631,628,324,41,614,558,337,323,39,615,559,338,701,699,702,700,563,343,475,61,399,564,344,62,476,397,60,345,565,477,398,342,562,474,64,395,340,560,472,65,396,341,561,473,63,394,569,349,481,67,390,570,350,482,68,388,571,351,483,66,389,568,348,480,70,393,566,346,478,71,391,567,347,479,69,392,665,669,668,671,531,264,190,212,599,532,265,213,188,600,214,263,533,189,601,267,530,186,211,598,268,528,187,209,596,266,529,185,210,597,537,270,181,203,605,538,271,179,204,606,539,269,180,205,607,536,273,184,206,604,534,274,182,207,602,535,272,183,208,603,686,687,682,680 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#9f23da9903d6ebc1c6f98cbe23264669be86f8e7144737b42fbccbf8aeddcd62, 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 19:20:40 · history