Equation 677 Database

← all  ·  ← by size  ·  ← size 705

Magma db6a274ef526…

magma db6a274ef526
Size
705
Isomorphism class hash
db6a274ef52653033b40a9976ed8620fb2392e9c75f4f70b09ea16d1fb80a601
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 21:24:21
Display reorder
660,450,318,372,258,462,451,319,373,259,463,452,320,374,260,464,321,375,261,465,453,322,454,376,262,466,323,455,377,263,467,256,378,448,316,460,379,449,317,257,461,380,447,315,255,459,444,381,312,252,456,445,382,313,253,457,446,383,314,254,458,679,682,683,675,106,534,178,279,426,107,535,179,280,427,105,536,177,281,428,537,174,278,429,102,538,103,175,276,430,539,104,176,277,431,285,169,97,532,424,170,98,533,286,425,168,96,531,287,423,100,172,528,284,420,101,173,529,282,421,99,171,530,283,422,670,672,664,668,294,342,187,71,354,295,343,188,69,355,296,344,186,70,356,345,190,67,357,297,346,298,191,68,358,347,299,189,66,359,62,185,292,340,352,183,293,341,60,353,184,291,339,61,351,288,181,336,65,348,289,182,337,63,349,290,180,338,64,350,680,677,681,685,612,614,134,619,613,620,622,132,627,621,628,630,133,635,629,638,137,643,636,637,646,645,135,651,644,654,653,136,659,652,603,140,597,598,596,138,605,606,611,604,139,589,590,595,588,564,143,565,569,568,572,141,574,579,573,582,142,580,587,581,703,700,704,701,402,42,147,390,414,403,43,148,391,415,404,44,149,392,416,45,146,393,417,405,46,406,144,394,418,47,407,145,395,419,388,153,400,40,412,154,401,41,389,413,155,399,39,387,411,396,152,36,384,408,397,150,37,385,409,398,151,38,386,410,693,691,692,690,438,366,5,202,330,439,367,3,203,331,440,368,4,201,332,369,0,198,333,441,370,442,2,199,334,371,443,1,200,335,193,11,436,364,328,9,437,365,194,329,10,435,363,192,327,432,7,360,196,324,433,8,361,197,325,434,6,362,195,326,663,665,662,661,233,28,159,226,22,231,29,160,227,23,232,27,161,225,21,24,158,222,18,229,25,230,156,223,19,26,228,157,224,20,217,165,239,34,13,166,237,35,218,14,167,238,33,216,12,235,164,30,220,16,236,162,31,221,17,234,163,32,219,15,695,689,696,694,558,510,92,486,250,559,511,90,487,251,560,512,91,488,249,513,95,489,246,561,514,562,93,490,247,515,563,94,491,248,484,87,556,508,241,88,557,509,485,242,89,555,507,483,240,552,86,504,480,244,553,84,505,481,245,554,85,506,482,243,687,688,674,686,616,618,51,615,617,624,626,52,623,625,632,634,53,631,633,642,50,639,641,640,650,648,48,647,649,658,656,49,655,657,599,57,600,602,601,58,608,610,607,609,59,592,594,591,593,570,56,571,566,567,576,54,578,575,577,584,55,586,583,585,699,702,697,698,131,546,117,522,498,129,547,118,523,499,130,548,119,524,500,549,116,525,501,127,550,128,114,526,502,551,126,115,527,503,520,108,122,544,496,109,120,545,521,497,110,121,543,519,495,125,111,540,516,492,123,112,541,517,493,124,113,542,518,494,671,666,667,669,474,306,213,80,270,475,307,214,78,271,476,308,215,79,272,309,212,83,273,477,310,478,210,81,274,311,479,211,82,275,75,204,472,304,268,205,473,305,76,269,206,471,303,77,267,468,207,300,74,264,469,208,301,72,265,470,209,302,73,266,678,684,676,673 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#ef4a4f27352a122a7b1088a6208971ffd57fb3858716fe27bd37fbc92d64744c, 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 21:24:22 · history