Equation 677 Database

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Magma 99bf2ae14a8a…

magma 99bf2ae14a8a
Size
705
Isomorphism class hash
99bf2ae14a8a571964d7246710c2d93a268937f4d30f7acd27dcfc07e6cf142b
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 20:42:18
Display reorder
660,215,59,312,226,523,313,213,227,524,57,314,58,214,225,525,311,218,62,229,522,309,216,60,230,520,310,217,61,228,521,65,221,232,318,529,219,63,233,319,530,220,64,231,320,531,68,224,235,317,528,66,222,236,315,526,316,67,223,234,527,666,662,661,669,420,141,93,78,86,94,418,79,84,142,95,143,419,80,85,96,423,144,77,82,97,421,145,75,83,98,422,146,76,81,147,415,69,99,92,416,148,70,100,90,417,149,71,101,91,150,414,72,102,88,151,412,73,103,89,104,152,413,74,87,685,691,688,689,475,182,257,40,48,255,476,41,49,180,256,181,477,39,50,260,474,178,43,47,258,472,179,44,45,259,473,177,42,46,188,481,38,252,54,482,186,36,253,55,483,187,37,254,56,184,480,34,251,53,185,478,35,249,51,250,183,479,33,52,670,667,671,665,463,336,547,159,583,548,464,160,584,337,549,338,465,161,585,546,462,335,162,582,544,460,333,163,580,545,461,334,164,581,342,469,157,553,589,470,343,158,554,590,471,344,156,555,591,341,468,153,552,588,339,466,154,550,586,551,340,467,155,587,680,673,678,675,393,170,9,559,348,10,394,560,349,168,11,169,395,561,350,12,392,166,558,347,13,390,167,556,345,14,391,165,557,346,176,399,565,15,354,400,174,566,16,355,401,175,567,17,356,172,398,564,18,353,173,396,562,19,351,20,171,397,563,352,663,668,672,664,607,243,511,631,451,512,608,632,452,244,513,245,609,633,453,510,606,246,630,450,508,604,247,628,448,509,605,248,629,449,241,613,637,517,457,614,242,638,518,458,615,240,639,519,459,237,612,636,516,456,238,610,634,514,454,515,239,611,635,455,695,700,697,699,402,365,357,383,7,358,403,384,8,366,359,364,404,385,6,360,405,368,382,3,361,406,369,380,4,362,407,367,381,5,371,408,389,363,376,655,372,654,653,652,659,370,658,656,657,374,409,388,378,0,375,410,386,379,2,377,373,411,387,1,701,703,702,704,439,25,487,116,128,488,440,114,126,26,489,24,441,115,127,486,438,21,112,124,484,436,22,113,125,485,437,23,111,123,31,445,107,493,119,446,32,105,494,117,447,30,106,495,118,27,444,110,492,122,28,442,108,490,120,491,29,443,109,121,693,698,696,694,286,210,278,300,595,276,287,301,596,211,277,212,285,302,597,274,289,209,299,594,275,290,207,297,592,273,288,208,298,593,201,292,306,284,601,293,202,307,282,602,291,203,308,283,603,204,295,305,280,600,205,296,303,281,598,279,206,294,304,599,681,682,676,684,571,129,535,643,324,536,572,644,325,130,537,131,573,645,326,534,570,132,642,323,532,568,133,640,321,533,569,134,641,322,135,577,649,541,330,578,136,650,542,331,579,137,651,543,332,138,576,648,540,329,139,574,646,538,327,539,140,575,647,328,674,683,677,679,427,193,619,499,270,620,428,500,271,194,621,192,429,501,272,618,426,189,498,269,616,424,190,496,267,617,425,191,497,268,199,433,505,625,261,434,200,506,626,262,435,198,507,627,263,195,432,504,624,264,196,430,502,622,265,623,197,431,503,266,692,687,690,686 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#cc21ed90a723dc84f76676d15ec858e33ef625916c28841b110b43408fa38d16, 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 20:42:19 · history