Equation 677 Database

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Magma f229ece04eca…

magma f229ece04eca
Size
381
Isomorphism class hash
f229ece04eca03b52dfeae2153e34455fcb00cd0657bc05542de4c24713bad4e
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 23:18:00
Display reorder
380,177,172,182,187,192,197,76,67,72,91,80,85,242,232,237,257,247,252,326,324,325,329,327,328,137,126,131,120,111,116,296,0,1,105,97,102,208,212,203,222,227,217,21,26,31,10,291,15,157,162,167,142,147,152,35,41,46,50,55,60,285,275,280,271,260,265,340,366,352,357,346,372,332,336,361,375,178,173,181,185,190,195,78,69,74,93,83,88,241,231,236,255,245,250,320,318,319,323,321,322,135,125,130,121,110,115,298,6,7,108,99,104,207,211,202,220,225,215,22,28,33,13,293,18,156,161,165,141,146,151,38,43,48,53,58,63,288,276,281,273,263,268,343,369,351,356,348,370,331,338,363,378,176,171,184,189,194,199,79,68,73,94,84,89,244,234,239,259,249,254,305,303,304,302,301,300,139,129,134,124,114,119,299,8,9,109,95,100,209,214,204,224,229,219,23,29,34,14,294,19,159,164,169,144,149,154,39,44,49,54,59,64,289,279,284,274,264,269,344,368,354,359,349,374,334,339,364,379,175,170,180,186,191,196,75,65,70,90,81,86,240,230,235,256,246,251,306,307,308,309,310,311,136,127,132,122,112,117,295,2,3,106,98,103,205,210,200,221,226,216,20,25,30,11,290,16,155,160,166,140,145,150,36,40,45,51,56,61,286,277,282,270,261,266,341,365,350,355,345,371,330,335,360,376,179,174,183,188,193,198,77,66,71,92,82,87,243,233,238,258,248,253,316,317,315,313,314,312,138,128,133,123,113,118,297,4,5,107,96,101,206,213,201,223,228,218,24,27,32,12,292,17,158,163,168,143,148,153,37,42,47,52,57,62,287,278,283,272,262,267,342,367,353,358,347,373,333,337,362,377 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#0c1c8b18119133fb8debdb5d149d6db1ac93e4c65e1bffaee2a0311d537b261b, 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 23:18:01 · history