Equation 677 Database

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Magma 2304953eee08…

magma 2304953eee08
Size
595
Isomorphism class hash
2304953eee08502bc16a918fbc31aa1368e442795059ba499d7c3e27449bd394
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
2026-10-06 19:24:19
Display reorder
272,270,271,273,274,275,281,280,279,276,278,277,350,349,351,352,353,348,356,355,357,358,359,354,360,365,361,362,363,364,556,555,592,594,593,40,39,41,36,37,38,73,72,74,77,75,76,248,247,246,249,250,251,42,44,43,47,45,46,230,232,231,228,229,227,55,54,56,57,58,59,52,51,53,50,48,49,70,69,71,66,67,68,61,60,62,65,63,64,396,401,397,398,399,400,382,381,383,378,379,380,389,388,384,385,386,387,403,402,404,405,406,407,366,371,367,368,369,370,377,376,372,373,374,375,395,394,390,391,392,393,553,513,538,517,527,522,543,548,533,569,564,560,579,589,575,584,21,23,22,20,18,19,202,201,203,200,199,198,240,241,242,245,243,244,26,25,24,28,29,27,222,239,223,225,226,224,11,10,9,7,8,6,17,16,15,12,13,14,30,32,31,35,33,34,209,208,207,205,204,206,343,342,344,345,346,347,317,316,312,313,314,315,326,325,327,328,329,324,341,340,336,337,338,339,334,333,335,330,331,332,306,311,307,308,309,310,318,323,319,320,321,322,554,510,539,519,529,524,544,549,534,571,566,561,581,591,576,586,154,153,155,150,151,152,172,171,173,170,168,169,267,269,268,265,266,264,156,158,157,161,159,160,217,216,218,221,219,220,148,147,149,144,145,146,166,165,167,164,162,163,178,177,179,174,175,176,195,194,196,193,192,197,502,507,503,504,505,506,487,486,488,489,484,485,304,303,305,300,301,302,500,499,501,496,497,498,492,491,493,494,495,490,482,481,483,478,479,480,296,295,297,298,299,294,552,514,537,518,528,523,542,547,532,570,565,559,580,590,574,585,123,125,124,122,120,121,136,135,137,134,132,133,259,258,260,263,261,262,187,188,186,191,189,190,213,215,214,210,212,211,117,119,118,116,114,115,130,129,131,128,126,127,141,143,142,140,138,139,2,0,1,3,4,5,476,475,477,472,473,474,455,454,456,457,458,459,291,290,292,293,288,289,470,469,471,466,467,468,462,461,463,464,465,460,450,449,451,452,453,509,283,287,282,284,285,286,550,512,535,516,526,520,541,546,531,567,563,557,577,587,572,583,98,97,96,100,101,99,83,82,81,78,79,80,254,253,252,255,256,257,95,94,93,91,92,90,238,237,236,233,234,235,106,105,107,102,103,104,180,181,182,185,183,184,85,84,86,87,88,89,108,110,109,112,113,111,413,412,408,409,410,411,435,434,436,437,432,433,446,445,447,448,443,444,415,414,416,417,418,419,425,424,420,421,422,423,430,429,431,426,427,428,440,439,441,438,508,442,551,511,536,515,525,521,540,545,530,568,562,558,578,588,573,582 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#f04ca8125d7ce546c7552606527b36663a07f654279810fba8dfdb3271b338ee, M = the submagma generated by {6, 36} (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 2026-10-06 19:24:20 · history