Equation 677 Database

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Magma 94461a5d1033…

magma 94461a5d1033
Size
705
Isomorphism class hash
94461a5d103388da85dcc953efb5ea1d119c4b5c40b5c36c27ed6ff747b30c30
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 20:00:41
Display reorder
660,67,66,68,69,70,71,64,65,63,60,61,62,394,395,393,390,391,392,385,386,384,388,389,387,335,333,334,331,332,330,326,324,325,329,327,328,272,270,271,275,273,274,267,268,269,266,264,265,209,207,208,205,206,204,215,213,214,211,212,210,662,665,669,681,110,109,108,112,113,111,115,116,114,118,119,117,608,606,607,611,609,610,603,604,605,602,600,601,10,11,9,6,7,8,0,2,1,4,5,3,485,483,484,481,482,480,491,489,490,487,488,486,543,544,545,542,540,541,549,550,551,548,546,547,683,686,687,698,413,412,411,408,409,410,418,419,417,414,415,416,239,237,238,235,236,234,230,228,229,233,231,232,298,299,297,294,295,296,289,290,288,292,293,291,350,348,349,353,351,352,356,354,355,359,357,358,40,41,39,36,37,38,46,47,45,42,43,44,661,670,668,680,614,613,612,616,617,615,619,620,618,622,623,621,552,553,554,555,556,557,558,559,560,561,562,563,14,12,13,17,15,16,20,18,19,23,21,22,492,493,494,495,496,497,498,499,500,501,502,503,124,125,123,120,121,122,130,131,129,126,127,128,671,675,677,689,452,451,450,454,455,453,449,447,448,445,446,444,28,29,27,24,25,26,34,35,33,30,31,32,628,629,627,624,625,626,634,635,633,630,631,632,572,570,571,575,573,574,567,568,569,566,564,565,507,508,509,506,504,505,513,514,515,512,510,511,663,664,666,682,55,54,56,57,58,59,52,53,51,48,49,50,338,336,337,341,339,340,344,342,343,347,345,346,217,218,216,220,221,219,223,224,222,226,227,225,397,398,396,400,401,399,403,404,402,406,407,405,280,281,279,276,277,278,286,287,285,282,283,284,692,696,695,701,166,165,167,164,162,163,156,157,158,159,160,161,170,168,169,173,171,172,176,174,175,179,177,178,182,180,181,185,183,184,188,186,187,191,189,190,147,148,149,146,144,145,153,154,155,152,150,151,140,138,139,143,141,142,135,136,137,134,132,133,699,700,703,704,459,461,460,457,458,456,467,465,466,463,464,462,89,87,88,85,86,84,95,93,94,91,92,90,526,527,525,522,523,524,517,518,516,520,521,519,644,642,643,647,645,646,639,640,641,638,636,637,577,578,576,580,581,579,583,584,582,586,587,585,691,693,694,702,380,379,378,382,383,381,377,375,376,373,374,372,252,253,254,255,256,257,258,259,260,261,262,263,314,312,313,317,315,316,320,318,319,323,321,322,433,434,432,436,437,435,439,440,438,442,443,441,75,76,77,74,72,73,81,82,83,80,78,79,667,676,673,688,96,98,97,101,99,100,104,102,103,107,105,106,588,589,590,591,592,593,594,595,596,597,598,599,468,469,470,471,472,473,474,475,476,477,478,479,531,532,533,530,528,529,537,538,539,536,534,535,650,648,649,653,651,652,656,654,655,659,657,658,672,674,678,690,366,368,367,371,369,370,363,364,365,362,360,361,309,310,311,308,306,307,300,301,302,303,304,305,195,196,197,194,192,193,201,202,203,200,198,199,245,243,244,241,242,240,251,249,250,247,248,246,423,424,425,422,420,421,429,430,431,428,426,427,679,685,684,697 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#b841b444f6b6a6329111833cc0cf1c9cdaf118d6968b1c3e99c4136ce1352ec2, M = {62} 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 20:00:42 · history