Equation 677 Database

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Magma 37ee73ab84e7…

magma 37ee73ab84e7
Size
705
Isomorphism class hash
37ee73ab84e7b2cb0bfc3dfcf6a553408f5d06b090ef0fd62cebc01351c076c4
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 21:08:26
Display reorder
660,6,523,532,524,529,7,483,492,484,489,8,503,512,504,509,450,9,453,451,452,463,10,471,464,468,423,11,431,424,428,4,652,643,644,649,5,612,603,604,609,3,632,623,624,629,572,1,563,564,569,592,0,583,584,589,552,2,543,544,549,701,702,694,685,16,520,531,530,535,17,481,491,490,495,15,501,511,510,515,447,12,444,443,446,461,13,470,469,473,420,14,430,429,433,22,651,640,650,655,23,611,601,610,615,21,631,621,630,635,571,18,560,570,575,591,19,580,590,595,551,20,541,550,555,698,691,693,690,277,234,329,250,253,278,235,327,251,254,276,236,328,249,252,237,280,325,246,256,238,281,326,247,257,239,279,324,248,255,283,335,232,241,259,284,333,233,242,260,282,334,231,240,258,331,286,228,244,262,332,287,229,245,263,330,285,230,243,261,676,675,664,681,211,182,175,196,365,212,180,176,197,363,210,181,174,195,364,185,214,178,192,361,183,215,179,193,362,184,213,177,194,360,209,173,188,202,371,207,171,186,203,369,208,172,187,201,370,169,205,191,198,367,170,206,189,199,368,168,204,190,200,366,670,665,662,683,31,536,537,538,521,32,496,497,498,480,30,516,517,518,500,456,34,454,455,448,478,35,474,475,460,436,33,434,435,421,29,657,656,658,641,27,617,616,618,600,28,637,636,638,620,577,25,576,578,561,597,26,596,598,581,557,24,556,558,540,695,703,699,687,95,522,528,534,539,93,482,488,494,499,94,502,508,514,519,449,91,457,458,459,462,92,476,477,479,422,90,437,438,439,86,648,642,654,659,84,608,602,614,619,85,628,622,634,639,568,89,562,574,579,588,87,582,594,599,548,88,542,554,559,689,696,688,700,156,525,533,526,527,157,485,493,486,487,158,505,513,506,507,440,159,445,441,442,465,160,472,466,467,425,161,432,426,427,162,653,645,646,647,163,613,605,606,607,164,633,625,626,627,573,165,565,566,567,593,166,585,586,587,553,167,545,546,547,704,686,692,697,74,401,63,317,48,72,399,64,315,49,73,400,65,316,50,397,77,62,313,51,398,75,60,314,52,396,76,61,312,53,80,69,407,323,54,78,70,405,321,55,79,71,406,322,56,68,83,403,319,57,66,81,404,320,58,67,82,402,318,59,669,666,679,682,99,413,38,139,116,100,411,36,140,114,101,412,37,138,115,409,98,41,142,119,410,96,39,143,117,408,97,40,141,118,105,44,419,137,111,106,42,417,135,112,107,43,418,136,113,47,104,415,133,110,45,102,416,134,108,46,103,414,132,109,673,680,671,684,225,389,272,377,293,226,387,270,375,291,227,388,271,376,292,385,224,275,373,289,386,222,273,374,290,384,223,274,372,288,216,267,395,383,299,217,268,393,381,297,218,269,394,382,298,266,219,391,379,295,264,220,392,380,296,265,221,390,378,294,661,672,677,674,130,353,341,305,144,131,351,339,303,145,129,352,340,304,146,349,126,337,301,147,350,127,338,302,148,348,128,336,300,149,121,347,359,311,150,122,345,357,309,151,120,346,358,310,152,343,124,355,307,153,344,125,356,308,154,342,123,354,306,155,678,663,667,668 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#d958d834958932013e293186c3edbca2299f39c5df5a243bf65f8d4f2fad3f22, M = {60} in E, B = magma#9878faa9b07066f62fc077f7c99df5b1f6f079c61c0cd7e7f5bbdb9bc181adbc. 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 21:08:27 · history