Equation 677 Database

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Magma 3b421cec5a07…

magma 3b421cec5a07
Size
381
Isomorphism class hash
3b421cec5a076cf6ddd13c329910e0d5366c9c8ab1450673202972e645dbd9ee
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 23:18:24
Display reorder
380,69,279,74,64,54,59,124,119,289,111,104,106,184,189,179,199,204,194,85,76,81,95,94,281,274,29,34,39,44,49,209,214,219,224,229,234,4,269,9,14,18,24,327,328,329,324,325,326,164,154,159,174,169,299,139,129,134,149,144,294,239,244,249,253,258,263,334,344,369,354,339,373,379,349,364,359,66,275,71,60,51,55,123,118,288,110,103,105,183,188,177,198,203,193,86,75,80,96,93,280,270,26,31,35,40,45,208,213,218,223,228,233,2,267,7,11,15,20,321,322,323,318,319,320,163,153,158,173,168,298,138,128,133,148,143,293,236,242,248,252,256,261,330,340,368,353,337,372,378,345,363,358,67,277,72,62,52,57,122,117,287,114,102,109,182,187,178,197,202,192,89,79,84,99,92,284,272,27,32,37,42,47,206,210,215,222,225,232,1,265,6,13,19,21,313,314,312,316,317,315,162,152,157,170,167,297,137,127,132,147,142,292,237,241,247,251,257,262,331,342,367,352,335,370,377,347,362,357,68,278,73,63,53,58,120,115,286,112,100,108,180,185,175,196,201,191,87,77,83,98,90,282,273,28,33,38,43,48,205,212,216,220,227,230,3,268,8,10,17,23,309,310,311,306,307,308,160,150,155,172,166,295,135,126,131,145,140,291,235,243,246,254,259,264,333,343,365,350,338,371,376,348,361,356,65,276,70,61,50,56,121,116,285,113,101,107,181,186,176,195,200,190,88,78,82,97,91,283,271,25,30,36,41,46,207,211,217,221,226,231,0,266,5,12,16,22,302,301,300,305,303,304,161,151,156,171,165,296,136,125,130,146,141,290,238,240,245,250,255,260,332,341,366,351,336,374,375,346,360,355 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#0c1c8b18119133fb8debdb5d149d6db1ac93e4c65e1bffaee2a0311d537b261b, M = {74} 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 23:18:25 · history