Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma 03fa81b6b8cd…

magma 03fa81b6b8cd
Size
705
Isomorphism class hash
03fa81b6b8cdb3f13d018299bb6c1e2385fb2ec87e0e0cca5ed4e34a578650d2
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 16:34:44
Display reorder
660,149,366,498,290,318,147,367,499,288,319,148,368,500,289,320,369,145,501,293,321,370,146,502,291,322,371,144,503,292,323,155,364,496,296,316,153,365,497,294,317,154,363,495,295,315,360,151,492,299,312,361,152,493,297,313,362,150,494,298,314,673,676,678,685,176,229,29,522,474,174,230,27,523,475,175,228,28,524,476,232,179,25,525,477,233,177,26,526,478,231,178,24,527,479,171,235,35,520,472,172,236,33,521,473,173,234,34,519,471,238,170,31,516,468,239,168,32,517,469,237,169,30,518,470,671,667,661,665,191,47,342,546,378,189,45,343,547,379,190,46,344,548,380,43,187,345,549,381,44,188,346,550,382,42,186,347,551,383,182,38,340,544,376,180,36,341,545,377,181,37,339,543,375,41,185,336,540,372,39,183,337,541,373,40,184,338,542,374,687,679,684,677,194,616,613,612,618,192,624,620,621,626,193,632,628,629,634,640,197,637,636,642,648,195,644,645,650,656,196,652,653,658,200,600,597,596,602,198,608,604,605,610,199,592,589,588,594,567,203,564,568,569,576,201,574,573,578,584,202,582,581,586,703,699,704,702,112,306,269,438,426,113,307,267,439,427,111,308,268,440,428,309,108,265,441,429,310,109,266,442,430,311,110,264,443,431,118,304,275,436,424,119,305,273,437,425,117,303,274,435,423,300,114,271,432,420,301,115,272,433,421,302,116,270,434,422,692,691,690,694,11,330,486,510,354,9,331,487,511,355,10,332,488,512,356,333,7,489,513,357,334,8,490,514,358,335,6,491,515,359,2,328,484,508,352,1,329,485,509,353,0,327,483,507,351,324,5,480,504,348,325,3,481,505,349,326,4,482,506,350,670,663,662,668,51,86,462,96,162,52,84,463,97,163,53,85,464,98,164,89,50,465,99,165,87,48,466,100,166,88,49,467,101,167,57,92,460,102,160,58,90,461,103,161,59,91,459,104,159,95,56,456,105,156,93,54,457,106,157,94,55,458,107,158,695,689,696,693,132,390,402,15,558,133,391,403,16,559,134,392,404,17,560,393,135,405,14,561,394,136,406,12,562,395,137,407,13,563,138,388,400,21,556,139,389,401,22,557,140,387,399,23,555,384,141,396,20,552,385,142,397,18,553,386,143,398,19,554,686,688,680,681,66,617,619,614,615,67,625,627,622,623,68,633,635,630,631,641,69,643,638,639,649,70,651,646,647,657,71,659,654,655,64,601,603,598,599,65,609,611,606,607,63,593,595,590,591,570,60,571,565,566,577,61,579,572,575,585,62,587,580,583,698,700,697,701,81,211,216,534,414,82,212,217,535,415,83,210,218,536,416,214,80,219,537,417,215,78,220,538,418,213,79,221,539,419,72,209,222,532,412,73,207,223,533,413,74,208,224,531,411,205,75,225,528,408,206,76,226,529,409,204,77,227,530,410,672,666,669,664,123,450,245,252,282,124,451,243,253,283,125,452,244,254,284,453,122,241,255,285,454,120,242,256,286,455,121,240,257,287,129,448,251,258,280,130,449,249,259,281,131,447,250,260,279,444,128,247,261,276,445,126,248,262,277,446,127,246,263,278,683,675,682,674 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#357eb5a07f294d712e4efb5d2eb529ba387854e51bbe679ac1cbb62e1e3b2fae, 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 16:34:45 · history