Equation 677 Database

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Magma 825a17ced5ee…

magma 825a17ced5ee
Size
705
Isomorphism class hash
825a17ced5ee25b473a1ff8a839c123021fb9d9e5843995d9bfc38105bdeb362
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 17:26:47
Display reorder
660,414,378,403,478,8,415,379,6,401,479,413,377,7,402,477,410,374,11,399,474,411,375,9,400,475,412,376,10,398,476,394,369,405,3,469,370,406,4,392,470,368,404,5,393,468,408,372,2,397,472,409,373,1,395,473,407,371,0,396,471,687,682,676,678,310,324,305,354,202,308,325,203,306,355,309,323,201,307,353,313,320,198,304,350,311,321,199,302,351,312,322,200,303,352,296,330,316,193,345,331,314,194,297,346,329,315,192,298,344,319,326,196,299,348,317,327,197,300,349,318,328,195,301,347,672,662,666,668,502,550,526,342,23,503,551,21,527,343,501,549,22,525,341,498,546,19,522,338,499,547,20,523,339,500,548,18,524,340,517,541,493,14,333,542,494,12,518,334,540,492,13,516,332,496,544,17,520,336,497,545,15,521,337,495,543,16,519,335,685,673,686,684,646,649,645,650,88,654,657,89,652,658,638,641,87,637,642,614,617,84,613,618,622,625,85,621,626,630,633,86,628,634,222,441,226,94,565,442,227,95,220,566,440,225,93,221,564,597,599,90,600,601,606,609,91,604,610,224,443,92,219,567,703,700,697,704,270,286,108,438,152,271,287,150,109,439,272,285,151,110,437,273,282,155,111,434,274,283,153,112,435,275,284,154,113,436,114,277,268,147,429,278,269,148,115,430,276,267,149,116,428,264,280,146,117,432,265,281,144,118,433,266,279,145,119,431,689,693,691,690,562,36,514,538,33,563,37,34,515,539,561,38,35,513,537,558,39,32,510,534,559,40,30,511,535,560,41,31,512,536,505,42,553,24,529,43,554,25,506,530,44,552,26,504,528,556,45,27,508,532,557,46,28,509,533,555,47,29,507,531,665,667,661,669,159,173,248,133,68,160,171,66,246,134,161,172,67,247,132,158,169,71,251,136,156,170,69,249,137,157,168,70,250,135,243,179,165,63,139,177,166,64,244,140,178,167,65,245,138,164,175,62,242,142,162,176,60,240,143,163,174,61,241,141,694,695,696,692,390,490,454,594,58,391,491,59,455,595,389,489,57,453,593,386,486,54,450,590,387,487,55,451,591,388,488,56,452,592,445,481,381,49,585,482,382,50,446,586,480,380,48,444,584,384,484,52,448,588,385,485,53,449,589,383,483,51,447,587,680,688,683,677,651,647,644,648,73,659,655,74,653,656,643,639,72,636,640,619,615,76,612,616,627,623,77,620,624,635,631,75,629,632,217,289,570,79,293,290,568,80,218,294,291,569,78,216,295,603,602,82,596,598,611,607,83,605,608,571,288,81,223,292,698,699,702,701,186,259,105,582,215,187,260,213,106,583,188,258,214,107,581,189,262,211,104,578,190,263,212,102,579,191,261,210,103,580,96,257,184,206,573,255,185,204,97,574,256,183,205,98,572,180,253,209,99,576,181,254,207,100,577,182,252,208,101,575,663,671,670,664,466,131,366,426,232,467,129,233,367,427,465,130,231,365,425,462,127,228,362,422,463,128,229,363,423,464,126,230,364,424,357,122,457,238,417,120,458,239,358,418,121,456,237,356,416,460,125,234,360,420,461,123,235,361,421,459,124,236,359,419,675,679,674,681 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#5751a2f21b762bdcbb8d7ca8109ff664440cd913db63bda4230c3be52dd8f5e2, M = {60} in E, B = magma#abfd8e025ce71b705594dbbe1465dc1c7328d12d30e12d07906d7138f9d583bc. 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 17:26:48 · history