Equation 677 Database

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Magma 256b9af9a051…

magma 256b9af9a051
Size
705
Isomorphism class hash
256b9af9a0512f8c615026d6559413a722719b9ca2c6a6b2ced86def4ead9146
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 16:27:32
Display reorder
660,3,418,289,285,472,4,419,290,286,473,5,417,288,287,471,2,292,414,284,468,415,293,1,282,469,0,416,283,470,291,276,295,424,9,478,277,296,425,10,479,278,294,423,11,477,298,279,420,8,474,6,299,280,421,475,297,281,422,7,476,679,676,675,686,32,496,172,157,233,30,497,173,158,231,31,495,171,156,232,35,168,492,160,229,493,169,33,161,230,34,494,159,228,170,163,178,502,27,239,164,179,503,28,237,162,177,501,29,238,174,166,498,26,235,24,175,167,499,236,176,165,500,25,234,664,668,666,663,188,307,508,544,430,186,308,509,545,431,187,306,507,543,429,191,504,310,540,426,311,505,189,541,427,190,309,542,428,506,550,514,305,183,436,551,515,303,184,437,549,513,304,185,435,510,546,301,182,432,180,511,547,302,433,512,548,300,181,434,677,674,682,680,143,338,466,332,328,141,336,467,330,329,142,337,465,331,327,139,462,341,335,324,339,463,140,333,325,138,340,334,326,464,646,648,647,134,651,654,656,655,132,659,638,640,639,133,643,614,612,613,137,616,135,624,623,620,627,632,631,628,136,635,704,700,701,699,358,65,256,520,556,359,63,257,521,557,357,64,255,519,555,354,252,61,516,552,62,253,355,517,553,356,60,518,554,254,526,262,71,364,562,527,263,69,365,563,525,261,70,363,561,258,522,67,360,558,361,259,523,68,559,260,524,66,362,560,694,691,692,689,123,568,211,312,454,124,569,212,313,455,125,567,210,314,453,122,214,564,315,450,565,215,120,316,451,121,566,317,452,213,318,209,574,129,460,319,207,575,130,461,320,208,573,131,459,205,321,570,128,456,126,206,322,571,457,204,323,572,127,458,665,671,669,670,42,382,373,16,532,43,383,374,17,533,44,381,372,15,531,45,376,378,12,528,379,377,46,13,529,47,380,14,530,375,22,371,388,40,538,23,369,389,41,539,21,370,387,39,537,367,18,384,36,534,37,368,19,385,535,366,20,386,38,536,693,690,696,695,200,604,586,442,394,198,605,587,443,395,199,603,585,441,393,203,582,600,438,390,601,583,201,439,391,202,602,440,392,584,448,592,610,195,400,449,593,611,196,401,447,591,609,197,399,588,444,606,194,396,192,589,445,607,397,590,446,608,193,398,673,688,678,685,59,598,227,217,580,57,599,225,218,581,58,597,226,216,579,55,223,594,220,576,595,224,56,221,577,54,596,219,578,222,644,645,650,50,649,653,652,658,48,657,636,637,642,49,641,618,617,619,53,615,51,622,621,626,625,630,629,634,52,633,702,703,698,697,244,348,484,406,155,245,349,485,407,153,243,350,483,405,154,240,480,351,402,151,352,481,241,403,152,242,353,404,150,482,412,490,346,250,146,413,491,347,251,144,411,489,345,249,145,486,408,342,246,149,247,487,409,343,147,488,410,344,248,148,661,672,662,667,77,99,89,271,109,75,100,87,272,110,76,101,88,270,108,73,85,98,274,112,96,86,74,275,113,72,97,273,111,84,269,95,105,83,115,267,93,106,81,116,268,94,107,82,114,91,265,104,79,118,80,92,266,102,119,90,264,103,78,117,681,683,687,684 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#3233330d12681148716a4d7ca0430e02a433d3f211b7945abf3bfa7e2eafe60e, 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 16:27:39 · history