Equation 677 Database

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Magma ef749dd436f7…

magma ef749dd436f7
Size
381
Isomorphism class hash
ef749dd436f7cb56fc5f15e62175b7d73c24ac67dc9e5da50bbe241961d63b33
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 23:37:30
Display reorder
380,164,159,154,299,174,169,302,301,300,305,303,304,93,98,283,78,83,88,289,124,119,109,111,101,294,149,144,134,139,129,28,273,31,38,43,48,277,53,58,63,68,73,14,4,9,268,18,23,184,189,179,199,204,194,209,214,219,224,229,234,238,249,244,264,254,259,333,373,363,343,353,338,359,369,348,379,160,155,152,297,172,167,311,309,310,308,306,307,92,97,282,77,82,87,287,121,115,106,113,103,292,147,142,132,135,125,25,271,32,37,41,47,278,52,57,62,67,72,12,2,7,266,19,21,180,185,177,195,200,190,206,211,215,221,226,230,237,247,242,262,252,257,332,372,360,340,352,336,355,367,346,377,162,157,150,295,170,166,314,312,313,317,315,316,91,95,280,75,80,85,285,122,117,105,110,102,290,146,141,130,136,127,26,270,33,36,42,46,275,50,55,61,66,71,10,0,5,265,16,20,182,186,176,196,202,192,207,212,217,222,227,232,235,245,241,261,251,256,331,371,361,341,350,335,357,365,345,375,163,158,153,298,173,168,326,324,325,329,327,328,94,99,284,79,84,89,288,123,118,108,114,104,293,148,143,133,138,128,29,274,34,39,44,49,279,54,59,64,69,74,13,3,8,269,15,24,183,188,178,198,203,193,208,213,218,223,228,233,239,248,243,263,253,258,334,374,362,344,354,339,358,368,349,378,161,156,151,296,171,165,318,319,320,321,322,323,90,96,281,76,81,86,286,120,116,107,112,100,291,145,140,131,137,126,27,272,30,35,40,45,276,51,56,60,65,70,11,1,6,267,17,22,181,187,175,197,201,191,205,210,216,220,225,231,236,246,240,260,250,255,330,370,364,342,351,337,356,366,347,376 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#9f798321a12a7c259b4293859981bcb696138223932c95126c1c0ef29c354b2f, M = {76} 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 23:37:31 · history