Equation 677 Database

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Magma ed2806fb4e9a…

magma ed2806fb4e9a
Size
595
Isomorphism class hash
ed2806fb4e9a9644254c33dc6da998e73474fa297c942db993c3513b42bb711b
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 594) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-07 22:28:40
Display reorder
36,35,31,32,33,34,122,121,123,124,119,120,26,25,27,28,29,30,301,300,302,303,304,305,333,335,334,332,330,331,516,522,575,563,588,239,238,172,240,236,237,174,141,142,143,144,140,96,95,91,92,93,94,77,76,78,220,219,168,216,218,217,167,74,75,105,104,106,107,108,226,154,183,184,185,186,153,178,177,179,150,175,176,360,362,361,363,364,365,491,490,489,487,488,486,262,261,263,259,258,260,432,434,433,435,436,437,492,494,493,497,495,496,415,414,416,417,418,419,449,448,447,445,446,444,407,406,405,404,402,403,548,550,527,525,521,526,528,520,576,585,574,593,573,565,581,591,11,10,6,7,8,9,51,52,53,54,55,50,4,3,5,0,1,2,128,127,129,130,125,126,99,98,100,101,102,103,59,58,60,56,57,211,198,159,195,196,197,158,231,230,170,227,228,229,503,501,502,499,500,498,291,293,292,290,288,289,455,454,453,451,452,450,506,505,507,504,509,508,462,464,463,467,465,466,268,267,269,264,265,266,373,372,374,375,376,377,461,460,459,458,456,457,533,532,514,549,551,515,531,511,589,569,584,568,566,557,556,553,63,62,64,65,66,61,23,18,19,20,21,22,47,46,48,49,44,45,136,135,137,138,139,134,112,111,113,114,109,110,146,145,147,148,149,257,252,247,253,254,255,225,251,250,246,256,248,249,279,281,280,276,277,278,440,439,438,485,442,441,294,443,295,296,297,298,349,348,350,352,353,351,358,357,359,354,355,356,395,394,393,391,392,390,389,388,387,385,386,384,413,412,411,410,408,409,542,524,519,512,541,539,538,540,552,594,586,562,582,583,564,570,38,43,39,40,41,42,37,190,187,188,155,189,205,163,206,162,203,204,235,234,171,133,131,132,118,117,115,116,232,233,156,191,192,193,157,194,165,207,208,209,210,164,243,242,244,173,245,241,371,370,369,368,366,367,400,399,401,396,397,398,347,346,345,343,344,342,324,326,325,327,328,329,282,284,283,287,285,286,336,338,337,341,339,340,480,484,299,482,483,481,378,380,379,381,382,383,547,544,535,518,513,510,517,536,590,560,587,558,592,567,559,561,14,13,15,16,17,12,97,223,224,169,221,222,201,161,202,199,160,200,215,214,166,71,72,73,67,70,68,69,212,213,181,180,151,182,152,24,85,90,86,87,88,89,84,83,79,80,81,82,312,314,313,315,316,317,319,318,320,321,322,323,429,431,430,428,426,427,421,420,422,424,425,423,309,311,310,308,306,307,273,275,274,272,270,271,476,475,474,478,479,477,473,472,471,470,468,469,534,523,543,545,546,537,530,529,572,554,571,555,577,580,578,579 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 595 = 35 + 5*112, 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, 5, B) with E = magma#5ad34b2f8758383b4965947b4701d5813e2a88f030dcc851453e9c1dba339352, M = the submagma generated by {24, 54} (35 elements) in E, B = magma#e549b5f8492c9b6b5ad530e3aa4f39c6e23d08645ebd1b36a3c2de2a5a23bac5. 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(5, 112): MacNeish's product over GF(16) x GF(7); GF(16) = F_2[x]/(x^4 + 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: 85.

last edited by qawbecrdtey at 2026-10-07 22:28:41 · history