Equation 677 Database

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Magma b11f6f60fd15…

magma b11f6f60fd15
Size
381
Isomorphism class hash
b11f6f60fd154ec5fb4232950fc56c31308dffa5323a352e16eca500d1c02bad
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 23:35:48
Display reorder
380,13,87,14,213,85,86,132,123,128,148,138,143,158,163,153,173,178,168,4,103,231,102,294,101,203,208,198,188,193,183,6,5,95,93,94,223,298,283,288,278,268,273,240,249,235,259,264,254,316,317,315,313,314,312,218,92,91,89,90,88,97,98,96,100,228,99,343,364,338,359,378,368,353,348,332,373,42,44,43,210,45,46,134,121,127,145,135,140,156,161,151,170,175,165,40,41,234,38,292,39,200,205,195,186,191,181,54,55,56,57,58,220,295,280,285,276,265,270,243,247,239,257,263,253,307,308,306,310,311,309,216,17,18,19,20,53,10,8,9,7,226,65,341,360,335,357,375,366,351,345,330,371,35,37,36,211,47,34,131,122,125,147,137,142,157,162,152,172,177,167,30,31,233,33,290,32,201,206,196,185,190,180,21,22,59,23,24,221,297,282,287,277,267,272,242,248,238,255,261,251,305,303,304,302,301,300,215,51,52,50,48,49,61,62,60,64,225,63,340,362,336,356,377,367,350,346,331,372,3,68,2,212,66,67,130,120,126,146,136,141,155,160,150,171,176,166,25,84,230,83,293,82,202,207,197,187,192,182,16,15,76,74,75,222,296,281,286,275,266,271,244,246,236,258,262,252,329,327,328,326,324,325,217,73,72,70,71,69,78,79,77,81,227,80,342,361,337,358,376,365,352,347,333,370,0,106,1,214,104,105,133,124,129,149,139,144,159,164,154,174,179,169,28,29,232,26,291,27,204,209,199,189,194,184,12,11,114,112,113,224,299,284,289,279,269,274,241,245,237,256,260,250,319,320,318,322,323,321,219,111,110,108,109,107,116,117,115,119,229,118,344,363,339,355,379,369,354,349,334,374 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#8e237b368ce49904371f47a0bbc192c3f49c4a8da81336b4c06fd9fdc3a5d75d, M = {69} 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 23:35:49 · history