Equation 677 Database

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Magma 0ed11b643ecc…

magma 0ed11b643ecc
Size
705
Isomorphism class hash
0ed11b643eccb22c5f69fef56cbd5ff0fe4d38dd3a05a64cf247feffec548fc3
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 19:48:21
Display reorder
660,312,395,400,384,444,313,393,401,385,445,399,311,386,446,394,398,308,403,383,443,396,404,309,381,441,397,310,402,382,442,318,406,390,375,435,319,407,391,376,436,317,405,392,377,437,409,314,389,378,438,410,315,387,379,439,408,316,388,380,440,662,664,670,668,87,242,250,37,176,88,243,248,38,177,249,86,39,178,244,245,90,253,40,179,246,251,91,41,180,247,89,252,42,181,85,256,240,43,182,83,254,241,44,183,84,255,239,45,184,259,81,236,46,185,257,82,237,47,186,258,80,238,48,187,686,687,685,689,335,551,575,432,491,333,552,576,433,492,577,334,434,493,553,550,338,574,431,490,548,572,336,429,488,549,337,573,430,489,330,566,542,423,482,331,567,543,424,483,332,568,544,425,484,569,329,545,426,485,570,327,546,427,486,571,328,547,428,487,663,666,671,669,55,194,92,267,6,56,195,93,268,4,94,57,266,5,196,197,58,95,270,2,198,96,59,271,3,199,60,97,269,0,53,98,192,265,12,54,99,193,263,10,52,100,191,264,11,101,49,188,261,8,102,50,189,262,9,103,51,190,260,7,673,677,679,680,210,515,456,597,279,211,516,457,598,280,458,209,599,278,517,514,206,455,596,282,512,453,207,594,283,513,208,454,595,281,201,447,506,588,277,202,448,507,589,275,200,449,508,590,276,450,204,509,591,273,451,205,510,592,274,452,203,511,593,272,672,661,665,667,418,503,622,468,623,419,504,624,469,625,626,417,470,627,505,502,421,621,467,620,500,616,422,465,617,501,420,618,466,619,416,325,494,459,322,414,326,495,460,323,415,324,496,461,321,1,412,497,462,320,613,413,498,463,612,615,411,499,464,614,694,697,698,696,111,477,587,70,481,112,654,655,653,652,659,110,658,657,656,478,114,586,73,67,479,584,115,71,68,480,113,585,72,69,109,578,475,77,62,107,579,476,78,63,108,580,474,79,61,581,105,471,76,65,582,106,472,74,66,583,104,473,75,64,703,701,704,702,129,213,161,647,646,130,214,162,648,649,163,128,650,651,212,216,132,160,644,645,217,158,133,641,640,215,131,159,642,643,135,152,219,629,628,136,153,220,630,631,134,154,218,632,633,155,138,222,635,634,156,139,223,637,636,157,137,221,638,639,700,699,693,695,116,373,290,563,296,117,374,291,564,297,292,118,565,298,372,369,119,293,562,299,370,294,120,560,300,371,121,295,561,301,122,288,364,554,302,123,289,365,555,303,124,287,363,556,304,284,125,367,557,305,285,126,368,558,306,286,127,366,559,307,678,681,675,682,146,35,539,165,226,147,36,540,166,224,541,148,164,225,34,31,149,538,168,229,32,536,150,169,227,33,151,537,167,228,144,530,26,171,232,145,531,27,172,230,143,532,25,170,231,533,140,29,174,235,534,141,30,175,233,535,142,28,173,234,684,674,676,683,13,343,355,527,609,14,344,356,528,610,354,15,529,611,342,339,16,351,526,608,340,352,17,524,606,341,18,353,525,607,19,361,349,518,600,20,362,350,519,601,21,360,348,520,602,357,22,345,521,603,358,23,346,522,604,359,24,347,523,605,688,690,692,691 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#aa12d1af20c50a7f712e8df2ac0f984d22557fb7db3e49cc75c20296525d3597, 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 19:48:22 · history