Equation 677 Database

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Magma e3f44491326a…

magma e3f44491326a
Size
381
Isomorphism class hash
e3f44491326ac27c2e5dcecbeb33a9563cd5a3e5152063ee5c27b64e151541da
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 23:46:52
Display reorder
380,244,239,249,251,256,14,4,24,269,18,304,305,303,300,302,260,9,301,84,89,79,284,99,94,124,119,289,114,104,109,129,134,139,144,294,149,179,184,189,194,199,204,216,206,211,231,221,226,164,154,159,174,169,299,29,34,39,44,49,274,74,279,69,59,64,54,364,349,334,354,339,374,368,344,359,379,240,235,245,252,257,10,0,21,266,15,306,307,308,309,310,262,5,311,81,86,75,281,95,90,120,115,285,111,101,106,125,132,136,142,290,146,175,181,187,191,197,201,218,208,213,233,223,228,162,150,157,170,165,296,26,31,36,40,45,270,70,276,65,56,60,51,360,346,330,351,336,371,366,340,355,375,242,236,247,250,255,12,2,20,265,16,325,326,324,328,329,261,7,327,80,85,76,280,96,91,122,117,288,112,100,107,127,131,137,141,291,145,176,182,186,192,196,202,215,205,210,230,220,225,160,151,156,171,166,295,25,30,35,41,46,271,71,275,66,55,61,50,361,345,331,350,335,370,365,341,356,376,243,238,248,254,259,13,3,23,268,17,315,316,317,312,313,264,8,314,83,88,78,283,98,93,123,118,287,113,103,108,128,133,138,143,293,148,178,183,188,193,198,203,219,209,214,234,224,229,163,153,158,173,168,298,28,33,38,43,48,273,73,278,68,58,63,53,363,348,333,353,338,373,369,343,358,378,241,237,246,253,258,11,1,22,267,19,322,323,321,319,320,263,6,318,82,87,77,282,97,92,121,116,286,110,102,105,126,130,135,140,292,147,177,180,185,190,195,200,217,207,212,232,222,227,161,152,155,172,167,297,27,32,37,42,47,272,72,277,67,57,62,52,362,347,332,352,337,372,367,342,357,377 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#e1df87152eb4e0a2aee101822e1e35ad774d7a93b5a84f6ade065ecc70777444, 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 23:46:53 · history