Equation 677 Database

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Magma afc9d69d0f35…

magma afc9d69d0f35
Size
381
Isomorphism class hash
afc9d69d0f3534cc8bec50a058fa455ff82cd0a02ac732c26f6093bcb8135faf
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:51:09
Display reorder
380,275,21,15,8,13,3,193,198,188,208,213,202,286,65,70,61,51,56,183,173,178,168,158,163,153,143,148,138,128,133,113,103,108,123,118,298,89,94,99,294,79,84,314,312,313,317,315,316,268,273,263,253,258,248,218,223,228,233,238,243,26,280,31,36,41,45,340,359,346,354,333,378,335,363,373,368,276,20,19,6,11,1,190,195,185,206,210,203,287,67,72,62,52,57,181,170,175,166,156,161,150,140,145,136,126,131,110,100,105,120,116,295,85,90,96,291,75,80,310,311,309,307,308,306,265,270,260,250,256,245,216,221,226,230,235,240,27,282,32,37,42,47,342,355,347,351,330,376,336,360,371,365,278,23,17,7,12,2,191,196,186,207,212,201,288,68,73,63,53,58,180,171,176,165,155,160,151,141,146,135,125,130,111,101,106,121,115,296,87,92,97,292,77,82,303,304,305,301,300,302,267,272,262,252,257,247,217,222,227,232,237,242,28,283,33,38,43,48,343,356,348,352,332,377,338,362,370,366,277,22,16,5,10,0,192,197,187,205,211,200,285,66,71,60,50,55,182,172,177,167,157,162,152,142,147,137,127,132,112,102,107,122,117,297,88,93,98,293,78,83,328,329,327,325,326,324,266,271,261,251,255,246,215,220,225,231,236,241,25,281,30,35,40,46,341,357,345,353,331,375,337,361,372,367,279,24,18,9,14,4,194,199,189,209,214,204,289,69,74,64,54,59,184,174,179,169,159,164,154,144,149,139,129,134,114,104,109,124,119,299,86,91,95,290,76,81,318,319,320,321,322,323,269,274,264,254,259,249,219,224,229,234,239,244,29,284,34,39,44,49,344,358,349,350,334,379,339,364,374,369 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 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#fac090d670a9c14492c148fae382a21bad3e48687c67df8555101af0e65e1711, M = {73} 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: 51.

last edited by qawbecrdtey at 2026-10-01 23:51:10 · history