Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma 08fbac370b93…

magma 08fbac370b93
Size
705
Isomorphism class hash
08fbac370b9391116eaefa2125836d507e8e0ed0e7f4ccc26e6cbd958e6d7b65
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 21:18:27
Display reorder
660,89,574,319,169,533,90,572,170,317,531,168,573,91,318,532,570,92,165,315,529,571,93,166,316,530,569,94,167,314,528,95,565,310,175,524,96,563,308,176,522,97,564,309,174,523,98,568,313,171,527,99,566,311,172,525,100,567,312,173,526,687,684,674,676,586,276,27,127,52,584,277,125,28,53,126,275,585,29,51,272,582,130,26,48,273,583,128,24,49,274,581,129,25,50,577,282,33,133,58,575,283,34,131,59,576,281,35,132,57,580,278,32,136,54,578,279,30,134,55,579,280,31,135,56,667,672,670,662,468,521,396,292,179,466,519,290,394,177,291,520,467,395,178,517,464,295,392,182,518,465,293,393,180,516,463,294,391,181,459,512,387,287,185,457,510,385,288,183,458,511,386,289,184,462,515,390,286,188,460,513,388,284,186,461,514,389,285,187,683,685,681,679,652,654,655,138,659,637,638,139,639,643,137,646,645,647,651,622,620,141,623,627,630,628,142,631,635,614,613,140,615,619,151,239,244,144,601,152,237,245,145,599,150,238,243,143,600,605,604,606,147,608,242,240,247,148,602,149,241,246,146,603,697,700,699,701,6,492,432,229,360,7,490,230,430,358,228,491,8,431,359,488,9,225,428,356,489,10,226,429,357,487,11,227,427,355,4,483,423,235,351,5,481,421,236,349,3,482,422,234,350,1,486,426,231,354,0,484,424,232,352,2,485,425,233,353,694,691,696,692,420,550,480,190,260,418,548,191,478,261,189,549,419,479,262,546,416,193,476,263,547,417,194,477,264,545,415,192,475,265,411,541,471,196,266,409,539,469,197,267,410,540,470,195,268,414,544,474,199,269,412,542,472,200,270,413,543,473,198,271,669,661,664,666,343,444,208,116,504,341,442,117,209,502,118,443,342,207,503,440,339,115,211,500,441,340,113,212,501,439,338,114,210,499,334,435,206,122,495,332,433,204,123,493,333,434,205,124,494,337,438,202,121,498,335,436,203,119,496,336,437,201,120,497,693,695,690,689,156,296,408,254,562,157,297,255,406,560,256,298,158,407,561,299,155,257,404,558,300,153,258,405,559,301,154,259,403,557,162,302,399,252,553,163,303,397,253,551,164,304,398,251,552,161,305,402,248,556,159,306,400,249,554,160,307,401,250,555,673,686,682,680,656,653,658,16,657,640,636,17,642,641,15,644,648,650,649,621,624,12,626,625,629,632,13,634,633,612,616,14,618,617,346,74,536,22,507,344,75,534,23,505,345,76,535,21,506,610,609,611,18,607,347,73,537,19,508,348,72,538,20,509,698,702,704,703,456,384,43,215,60,454,382,213,44,61,214,383,455,42,62,380,452,218,46,63,381,453,216,47,64,379,451,217,45,65,447,375,41,221,66,445,373,39,219,67,446,374,40,220,68,450,378,37,224,69,448,376,38,222,70,449,377,36,223,71,663,671,665,668,372,323,598,111,88,370,324,112,596,86,110,325,371,597,87,322,368,107,594,84,320,369,108,595,85,321,367,109,593,83,363,329,589,102,79,361,330,587,103,77,362,331,588,101,78,366,328,592,105,82,364,326,590,106,80,365,327,591,104,81,675,677,678,688 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#e6bbf558fb3ffab686d395ed44cee4ecb6da0873fc29bc1527bdf36d2fd1603f, 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 21:18:28 · history