Equation 677 Database

← all  ·  ← by size  ·  ← size 381

Magma 97a2d3ce2bf1…

magma 97a2d3ce2bf1
Size
381
Isomorphism class hash
97a2d3ce2bf115a904fb29c35e6d9be00c4172c0fa6bc7f461eb615476c609af
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 23:34:08
Display reorder
380,294,284,244,254,264,274,308,309,310,311,306,307,24,25,26,27,28,29,276,286,299,246,256,266,32,33,34,35,30,31,99,100,101,96,97,98,206,216,226,236,186,196,51,52,53,48,49,50,104,105,106,107,102,103,224,234,184,194,204,214,55,54,56,57,58,59,335,338,334,361,371,339,363,346,347,376,292,282,242,252,262,272,301,300,302,303,304,305,14,15,16,17,12,13,278,288,297,248,258,268,23,18,19,20,21,22,179,174,175,176,177,178,208,218,228,238,188,198,164,165,166,167,162,163,170,171,172,173,168,169,222,232,182,192,202,212,161,160,156,157,158,159,333,356,332,364,373,357,366,358,359,378,296,287,247,257,267,277,326,327,328,329,324,325,119,114,115,116,117,118,270,281,291,240,250,260,110,111,112,113,108,109,73,74,75,76,77,72,200,210,220,230,181,191,142,143,138,139,140,141,78,79,80,81,82,83,227,237,187,197,207,217,133,132,134,135,136,137,348,353,349,367,377,352,369,343,342,370,295,285,245,255,265,275,313,314,315,316,317,312,86,87,88,89,84,85,279,289,298,249,259,269,95,90,91,92,93,94,146,147,148,149,144,145,209,219,229,239,189,199,3,4,5,1,0,2,153,154,155,150,151,152,225,235,185,195,205,215,7,6,8,9,10,11,345,330,344,362,375,331,368,354,355,379,293,283,243,253,263,273,322,323,318,319,320,321,63,64,65,60,61,62,271,280,290,241,251,261,67,68,69,70,71,66,128,129,130,131,126,127,201,211,221,231,180,190,43,44,45,46,47,42,123,124,125,120,121,122,223,233,183,193,203,213,39,38,40,41,36,37,340,337,341,360,374,336,365,351,350,372 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#83cf1f35d4fb7256f5d65d48e163e6c0239fd3c4b75a82ae41fd7ea0fe92a1c5, M = {75} 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 23:34:09 · history