Equation 677 Database

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Magma 7cc63fc12c93…

magma 7cc63fc12c93
Size
705
Isomorphism class hash
7cc63fc12c93a0b295eae89ade77857fe0aeee3dfcfb3c6d4073db9e4feb40f1
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 21:47:55
Display reorder
660,387,389,388,385,386,384,395,393,394,391,392,390,404,402,403,407,405,406,399,400,401,398,396,397,412,413,411,408,409,410,418,419,417,414,415,416,381,382,383,380,378,379,372,373,374,375,376,377,34,35,33,30,31,32,25,26,24,28,29,27,662,671,665,669,567,569,568,565,566,564,575,573,574,571,572,570,584,582,583,587,585,586,579,580,581,578,576,577,591,592,593,590,588,589,597,598,599,596,594,595,605,603,604,601,602,600,611,609,610,607,608,606,473,471,472,469,470,468,479,477,478,475,476,474,687,690,688,692,259,258,260,261,262,263,256,257,255,252,253,254,270,271,272,273,274,275,268,269,267,264,265,266,232,233,231,228,229,230,238,239,237,234,235,236,244,245,243,240,241,242,250,251,249,246,247,248,19,20,18,22,23,21,17,15,16,13,14,12,661,666,667,668,628,627,629,626,624,625,633,634,635,632,630,631,644,642,643,647,645,646,639,640,641,638,636,637,651,652,653,650,648,649,657,658,659,656,654,655,612,613,614,615,616,617,618,619,620,621,622,623,480,481,482,483,484,485,486,487,488,489,490,491,674,681,675,682,493,492,494,495,496,497,498,499,500,501,502,503,505,506,504,508,509,507,511,512,510,514,515,513,527,525,526,523,524,522,518,516,517,521,519,520,539,537,538,535,536,534,530,528,529,533,531,532,421,422,420,424,425,423,427,428,426,430,431,429,664,672,663,670,181,180,182,183,184,185,186,187,188,189,190,191,193,194,192,196,197,195,199,200,198,202,203,201,215,213,214,211,212,210,206,204,205,209,207,208,227,225,226,223,224,222,218,216,217,221,219,220,46,47,45,42,43,44,37,38,36,40,41,39,693,696,698,700,81,83,82,79,80,78,74,72,73,77,75,76,94,95,93,90,91,92,85,86,84,88,89,87,98,96,97,101,99,100,104,102,103,107,105,106,110,108,109,113,111,112,116,114,115,119,117,118,65,63,64,61,62,60,71,69,70,67,68,66,701,702,703,704,138,140,139,143,141,142,135,136,137,134,132,133,551,549,550,547,548,546,542,540,541,545,543,544,435,436,437,434,432,433,441,442,443,440,438,439,447,448,449,446,444,445,453,454,455,452,450,451,120,121,122,123,124,125,126,127,128,129,130,131,694,695,697,699,326,325,324,328,329,327,331,332,330,334,335,333,341,339,340,337,338,336,347,345,346,343,344,342,354,355,356,357,358,359,352,353,351,348,349,350,366,367,368,369,370,371,364,365,363,360,361,362,169,170,168,172,173,171,175,176,174,178,179,177,676,680,677,684,49,48,50,51,52,53,54,55,56,57,58,59,3,4,5,2,1,0,9,10,11,8,6,7,460,461,459,456,457,458,466,467,465,462,463,464,144,145,146,147,148,149,150,151,152,153,154,155,553,554,552,556,557,555,559,560,558,562,563,561,673,679,678,683,312,314,313,317,315,316,320,318,319,323,321,322,277,278,276,280,281,279,283,284,282,286,287,285,299,297,298,295,296,294,290,288,289,293,291,292,311,309,310,307,308,306,302,300,301,305,303,304,167,165,166,163,164,162,158,156,157,161,159,160,685,689,686,691 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#f6a46900b44d5ece02211ebe9219e83165d75916b83af00bea786f1bcca6cac9, 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 21:47:55 · history