Equation 677 Database

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Magma 31f1003dc515…

magma 31f1003dc515
Size
705
Isomorphism class hash
31f1003dc515546395e2105a4716695f618f93e0ab7cf28186aedc3dbece6ca9
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 16:32:42
Display reorder
660,299,539,408,157,468,300,469,540,409,158,301,470,541,410,156,302,538,467,407,153,303,536,465,405,154,304,537,466,406,155,297,530,459,399,163,298,531,460,400,164,296,532,461,401,162,533,293,462,402,159,403,534,294,463,160,535,295,464,404,161,665,671,667,670,147,456,209,82,515,148,516,457,210,83,149,517,458,211,81,150,455,514,212,85,151,453,512,213,86,152,454,513,214,84,145,447,506,215,88,146,448,507,216,89,144,449,508,217,87,450,141,509,218,91,219,451,142,510,92,452,143,511,220,90,689,685,687,686,178,503,261,278,444,179,445,504,262,279,177,446,505,260,280,181,502,443,257,277,182,500,441,258,275,180,501,442,259,276,184,494,435,267,269,185,495,436,268,270,183,496,437,266,271,497,187,438,263,272,264,498,188,439,273,499,186,440,265,274,662,661,666,668,230,480,345,98,527,231,528,481,346,96,232,529,482,347,97,229,479,526,348,94,227,477,524,349,95,228,478,525,350,93,221,471,518,343,104,222,472,519,344,102,223,473,520,342,103,474,224,521,339,100,340,475,225,522,101,476,226,523,341,99,682,673,677,676,201,315,326,621,360,202,361,316,327,622,200,362,314,328,623,197,311,359,325,620,198,312,357,323,618,199,313,358,324,619,207,306,351,317,612,208,307,352,318,613,206,305,353,319,614,309,203,354,320,615,321,310,204,355,616,308,205,356,322,617,663,672,664,669,249,551,575,609,45,250,46,552,576,610,248,47,553,577,611,245,550,48,574,608,246,548,49,572,606,247,549,50,573,607,255,542,51,566,600,256,543,52,567,601,254,544,53,568,602,545,251,54,569,603,570,546,252,55,604,547,253,56,571,605,697,698,693,695,77,493,335,599,489,75,654,655,653,652,76,656,657,659,658,80,13,490,336,596,78,14,491,337,597,79,12,492,338,598,72,20,487,333,591,73,18,488,334,592,74,19,486,332,590,16,71,483,329,594,330,17,69,484,595,15,70,485,331,593,704,701,703,702,60,432,647,646,563,61,564,433,649,648,62,565,434,650,651,59,431,562,644,645,57,429,560,641,640,58,430,561,643,642,66,423,554,191,196,67,424,555,192,194,68,425,556,193,195,426,65,557,190,189,637,427,63,558,636,428,64,559,638,639,700,699,696,694,11,36,420,633,397,9,398,37,421,634,10,396,38,422,635,7,35,393,419,632,8,33,394,417,630,6,34,395,418,631,2,42,388,411,624,1,43,389,412,625,0,44,387,413,626,41,5,391,414,627,415,39,3,392,628,40,4,390,416,629,674,684,681,675,170,134,587,283,123,168,124,132,588,281,169,125,133,589,282,166,130,126,586,286,167,131,127,584,284,165,129,128,585,285,176,140,121,578,289,174,138,122,579,287,175,139,120,580,288,136,172,117,581,292,582,137,173,118,290,135,171,119,583,291,680,679,678,683,112,379,239,24,374,113,372,380,240,25,111,373,378,241,26,115,375,370,242,23,116,376,371,243,21,114,377,369,244,22,110,385,365,237,30,108,386,363,238,31,109,384,364,236,32,381,106,368,233,29,234,382,107,366,27,383,105,367,235,28,688,690,691,692 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#34f20f8c77c0cbdeb0b8c0e60587a50e7d9ef4f1dbdd588ea7161aafd1a43efd, 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 16:32:43 · history