Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma 2f2f6a17cff7…

magma 2f2f6a17cff7
Size
705
Isomorphism class hash
2f2f6a17cff7bc78daf3f1cefa042bb170906ab3f6ac6f4f081d664961c5c0c5
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 20:42:07
Display reorder
660,519,30,355,391,347,356,520,392,348,31,357,32,521,393,346,354,518,33,390,350,352,516,34,388,351,353,517,35,389,349,28,525,397,361,345,526,29,398,362,343,527,27,399,363,344,24,524,396,360,341,25,522,394,358,342,359,26,523,395,340,675,680,678,683,260,315,379,403,170,380,261,404,171,313,381,314,259,405,169,378,256,311,402,173,376,257,312,400,174,377,258,310,401,172,306,266,409,385,168,267,304,410,386,166,265,305,411,387,167,309,262,408,384,164,307,263,406,382,165,383,308,264,407,163,662,664,663,667,271,181,539,367,319,540,272,368,320,182,541,183,273,369,321,538,270,184,366,318,536,268,185,364,316,537,269,186,365,317,179,277,373,545,325,278,180,374,546,326,279,178,375,547,327,175,276,372,544,324,176,274,370,542,322,543,177,275,371,323,676,679,684,674,237,5,492,145,531,493,235,146,532,3,494,4,236,147,533,491,240,0,148,530,489,238,2,149,528,490,239,1,150,529,11,637,636,640,642,644,9,645,648,650,652,10,653,656,658,7,628,629,632,633,8,241,243,495,534,488,6,242,144,535,701,698,704,703,463,127,55,196,203,56,464,197,204,128,54,126,465,198,202,58,462,130,195,199,59,460,131,193,200,57,461,129,194,201,125,469,187,53,209,470,123,188,51,210,471,124,189,52,208,121,468,190,49,205,122,466,191,50,206,48,120,467,192,207,693,689,692,691,225,141,415,575,86,416,223,576,84,142,417,143,224,577,85,414,228,140,574,89,412,226,138,572,87,413,227,139,573,88,132,231,581,421,92,229,133,582,422,90,230,134,583,423,91,135,234,580,420,95,136,232,578,418,93,419,137,233,579,94,668,672,665,661,20,112,44,611,610,42,18,613,612,113,43,111,19,614,615,47,23,108,608,609,45,21,109,605,604,46,22,110,606,607,118,15,623,39,622,16,119,624,40,625,17,117,626,41,627,114,14,620,38,621,115,12,617,36,616,37,116,13,618,619,696,695,690,694,595,280,451,331,71,452,596,332,69,281,453,282,597,333,70,450,594,283,330,67,448,592,284,328,68,449,593,285,329,66,286,601,337,457,62,602,287,338,458,60,603,288,339,459,61,289,600,336,456,65,290,598,334,454,63,455,291,599,335,64,673,677,682,687,484,301,475,499,587,476,485,500,588,302,477,303,486,501,589,474,483,300,498,586,472,481,298,496,584,473,482,299,497,585,292,639,641,638,643,647,293,649,646,651,655,294,657,654,659,295,634,635,630,631,296,487,502,478,590,479,297,480,503,591,702,700,697,699,507,153,247,563,439,248,508,564,440,151,249,152,509,565,441,246,506,156,562,438,244,504,154,560,436,245,505,155,561,437,159,513,569,253,445,514,157,570,254,446,515,158,571,255,447,162,512,568,252,444,160,510,566,250,442,251,161,511,567,443,666,671,670,669,97,80,214,551,427,215,98,552,428,78,216,79,96,553,429,213,100,83,550,426,211,101,81,548,424,212,99,82,549,425,75,103,557,220,433,104,76,558,221,434,102,77,559,222,435,74,106,556,219,432,72,107,554,217,430,218,73,105,555,431,681,685,688,686 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#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 20:42:08 · history