Equation 677 Database

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Magma 0a71855ceb29…

magma 0a71855ceb29
Size
705
Isomorphism class hash
0a71855ceb29955d4cdabaf0885dce12cd92ff32d0bae4a0c3ef2f1bfc730f19
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 21:53:39
Display reorder
660,550,174,189,95,460,551,93,175,190,461,176,94,549,191,459,546,177,91,188,456,547,178,92,186,457,548,179,90,187,458,180,195,556,101,466,181,196,557,99,467,182,197,555,100,465,194,183,552,97,462,192,184,553,98,463,193,185,554,96,464,681,680,683,686,256,279,245,88,300,257,89,280,243,301,281,87,255,244,302,252,278,84,241,303,253,276,85,242,304,254,277,86,240,305,270,236,247,79,298,271,234,248,80,299,272,235,246,78,297,239,273,250,82,294,237,274,251,83,295,238,275,249,81,296,669,672,665,664,39,310,562,265,436,40,266,311,563,437,309,264,41,561,435,38,306,268,558,432,36,307,269,559,433,37,308,267,560,434,316,568,30,263,442,317,569,31,261,443,315,567,32,262,441,564,312,33,259,438,565,313,34,260,439,566,314,35,258,440,673,679,687,684,352,343,25,124,608,353,125,344,26,606,342,123,351,24,607,348,346,120,28,611,349,347,121,29,609,350,345,122,27,610,644,645,646,115,651,652,653,654,116,659,636,637,638,114,643,613,612,614,118,616,621,620,622,119,627,628,629,630,117,635,697,704,698,702,496,472,574,200,73,497,198,473,575,74,471,199,495,573,72,492,468,203,570,76,493,469,201,571,77,494,470,202,572,75,478,580,502,206,71,479,581,503,204,69,477,579,501,205,70,576,474,498,209,67,577,475,499,207,68,578,476,500,208,66,691,695,692,696,107,54,424,151,50,105,152,55,425,48,56,150,106,423,49,103,57,154,420,53,104,58,155,421,51,102,59,153,422,52,60,430,113,157,45,61,431,111,158,46,62,429,112,156,47,426,63,109,160,44,427,64,110,161,42,428,65,108,159,43,667,661,670,662,379,412,210,133,508,380,134,413,211,509,411,132,378,212,507,382,408,136,213,504,383,409,137,214,505,381,410,135,215,506,418,216,385,131,514,419,217,386,129,515,417,218,384,130,513,219,414,388,127,510,220,415,389,128,511,221,416,387,126,512,690,693,689,694,364,334,13,142,400,365,143,335,14,401,333,141,363,12,399,360,330,138,16,396,361,331,139,17,397,362,332,140,15,398,340,19,370,148,406,341,20,371,149,407,339,18,369,147,405,22,336,366,144,402,23,337,367,145,403,21,338,368,146,404,676,678,677,674,520,376,357,231,394,521,232,377,358,395,375,233,519,359,393,516,372,230,356,390,517,373,228,354,391,518,374,229,355,392,648,647,650,222,649,656,655,658,223,657,640,639,642,224,641,617,618,619,225,615,623,624,626,226,625,631,632,634,227,633,700,701,703,699,538,484,448,286,586,539,287,485,449,587,483,285,537,447,585,534,480,282,444,582,535,481,283,445,583,536,482,284,446,584,490,454,544,292,592,491,455,545,293,593,489,453,543,291,591,450,486,540,288,588,451,487,541,289,589,452,488,542,290,590,666,671,668,663,526,9,598,173,322,527,171,10,599,323,11,172,525,597,321,522,8,169,594,318,523,6,170,595,319,524,7,168,596,320,1,604,532,164,328,0,605,533,162,329,2,603,531,163,327,600,3,528,167,324,601,4,529,165,325,602,5,530,166,326,685,675,682,688 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#fb895e2582be84c8b2721db1499636a6dec5ebe66e3b80b47964e64d8130d57b, 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 21:53:40 · history