Equation 677 Database

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Magma e3c4e6f42bf3…

magma e3c4e6f42bf3
Size
399
Isomorphism class hash
e3c4e6f42bf33e204d0e297070e5350ef9bff713b1658272624b174c7da2723a
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 398) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-06 17:32:04
Display reorder
255,256,257,258,259,260,252,253,254,264,265,266,267,268,269,261,262,263,379,327,273,291,309,328,274,292,310,329,275,293,311,330,276,294,312,331,277,295,313,332,278,296,314,324,270,288,306,325,271,289,307,326,272,290,308,282,336,300,318,283,337,301,319,284,338,302,320,285,339,303,321,286,340,304,322,287,341,305,323,279,333,297,315,280,334,298,316,281,335,299,317,391,385,386,392,199,185,168,130,200,186,169,131,201,187,170,132,202,188,162,133,203,180,163,134,204,181,164,126,205,182,165,127,206,183,166,128,198,184,167,129,194,208,177,139,195,209,178,140,196,210,179,141,197,211,171,142,189,212,172,143,190,213,173,135,191,214,174,136,192,215,175,137,193,207,176,138,383,389,390,384,228,46,73,60,229,47,74,61,230,48,75,62,231,49,76,54,232,50,77,55,233,51,78,56,225,52,79,57,226,53,80,58,227,45,72,59,39,221,82,69,40,222,83,70,41,223,84,71,42,224,85,63,43,216,86,64,44,217,87,65,36,218,88,66,37,219,89,67,38,220,81,68,388,398,397,387,349,154,112,343,351,155,113,345,353,156,114,346,355,157,115,348,357,158,116,350,359,159,108,352,342,160,109,354,344,161,110,356,347,153,111,358,147,367,121,360,148,369,122,362,149,371,123,364,150,372,124,366,151,374,125,368,152,376,117,370,144,361,118,373,145,363,119,375,146,365,120,377,394,395,396,393,237,33,92,13,238,34,93,14,239,35,94,15,240,27,95,16,241,28,96,17,242,29,97,9,234,30,98,10,235,31,90,11,236,32,91,12,26,246,101,6,18,247,102,7,19,248,103,8,20,249,104,1,21,250,105,0,22,251,106,2,23,243,107,3,24,244,99,4,25,245,100,5,378,381,380,382 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 399 = 19 + 5*76, 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#82a35c78c79e9ca1131d5b2db2d4981dbb5b7d3bd5cac5eb5a2f2461c98410ee, M = the submagma generated by {0} (19 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, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + 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: 21.

last edited by qawbecrdtey at 2026-10-06 17:32:05 · history