Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma bc3d790c1443…

magma bc3d790c1443
Size
705
Isomorphism class hash
bc3d790c14434a720e36a1ffdb8108fe450e502c670141d1a6fea503eeca01cd
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 21:21:00
Display reorder
660,83,46,307,557,34,81,35,47,305,555,82,33,45,306,556,42,79,30,303,553,43,80,31,304,554,44,78,32,302,552,74,37,25,298,548,26,38,296,72,546,24,36,297,73,547,40,28,301,77,551,41,29,299,75,549,39,27,300,76,550,675,684,674,686,95,504,198,185,170,96,168,502,199,183,97,169,503,200,184,500,98,166,197,188,501,99,167,195,186,499,100,165,196,187,93,495,161,204,191,159,493,205,94,189,160,494,206,92,190,498,164,203,89,194,496,162,201,90,192,497,163,202,91,193,665,672,667,668,310,379,545,451,403,308,401,377,543,449,309,402,378,544,450,375,313,399,541,447,376,311,400,542,448,374,312,398,540,446,316,370,394,536,442,392,368,534,314,440,393,369,535,315,441,373,397,539,319,445,371,395,537,317,443,372,396,538,318,444,683,681,677,678,128,653,652,659,656,129,640,637,636,643,130,648,645,644,651,621,127,624,620,627,628,125,632,629,635,613,126,616,612,619,134,139,466,145,601,464,137,146,135,599,465,138,144,136,600,604,607,605,133,608,140,467,142,131,602,141,468,143,132,603,701,700,704,699,55,237,480,246,516,56,514,238,478,247,54,515,239,479,248,240,58,512,476,245,241,59,513,477,243,242,57,511,475,244,53,235,507,471,252,505,236,469,51,253,506,234,470,52,254,231,510,474,49,251,232,508,472,50,249,233,509,473,48,250,690,694,695,692,324,113,17,439,463,325,461,114,15,437,323,462,115,16,438,116,320,459,13,435,117,321,460,14,436,118,322,458,12,434,330,119,454,23,430,452,120,21,331,428,453,121,22,329,429,122,457,19,326,433,123,455,20,327,431,124,456,18,328,432,661,664,671,666,347,528,586,492,264,348,265,526,584,490,349,266,527,585,491,524,346,263,582,488,525,344,261,583,489,523,345,262,581,487,353,519,255,577,483,256,517,575,354,481,257,518,576,355,482,522,258,580,352,486,520,259,578,350,484,521,260,579,351,485,696,691,693,689,274,367,415,106,569,272,567,365,413,104,273,568,366,414,105,363,277,565,411,102,364,275,566,412,103,362,276,564,410,101,280,358,560,406,112,558,356,404,278,110,559,357,405,279,111,361,563,409,283,108,359,561,407,281,109,360,562,408,282,107,679,687,676,685,8,657,655,654,658,6,642,641,639,638,7,650,649,647,646,625,11,626,623,622,633,9,634,631,630,617,10,618,615,614,3,531,572,88,269,570,529,86,4,267,571,530,87,5,268,610,611,609,2,606,532,573,85,1,270,533,574,84,0,271,698,697,702,703,156,181,213,391,224,157,222,182,214,389,158,223,180,215,390,177,155,220,216,387,178,153,221,217,388,179,154,219,218,386,147,172,230,211,382,228,173,212,148,380,229,171,210,149,381,175,226,207,150,385,176,227,208,151,383,174,225,209,152,384,669,663,670,662,335,427,60,285,598,336,596,425,61,286,337,597,426,62,284,423,334,594,63,288,424,332,595,64,289,422,333,593,65,287,341,418,589,66,291,587,416,67,342,292,588,417,68,343,290,421,592,69,340,294,419,590,70,338,295,420,591,71,339,293,682,673,680,688 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#ea8bb88472b4cb0aad957f1394df72437c069594286fecb60b6451f1d57bec9b, 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 21:21:01 · history