Equation 677 Database

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Magma 8875ba36a20d…

magma 8875ba36a20d
Size
321
Isomorphism class hash
8875ba36a20d43d41f38c88f01f97d91e081f5243b290579106197755e289782
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 320) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:04:48
Display reorder
300,36,96,113,136,120,37,97,111,137,121,38,98,112,135,122,99,39,109,132,123,100,110,133,124,40,101,41,108,134,125,42,119,102,142,126,43,117,103,143,127,44,118,104,141,128,115,45,105,138,129,139,116,46,106,130,114,47,107,140,131,305,303,302,301,250,269,268,270,271,251,272,273,274,275,249,265,264,267,266,252,246,253,254,255,256,257,258,259,247,260,248,261,263,262,241,292,293,294,295,242,297,296,299,298,240,288,289,291,290,276,244,277,278,279,282,280,245,281,283,285,243,284,286,287,319,317,318,320,65,9,208,225,224,63,10,209,226,227,64,11,207,223,222,8,61,204,216,217,6,205,218,219,62,7,60,206,220,221,71,214,1,236,237,69,215,0,238,239,70,213,2,235,234,210,67,3,229,228,230,211,68,4,231,212,66,5,232,233,311,312,313,314,73,158,172,149,53,74,156,173,147,51,72,157,171,148,52,161,76,168,145,49,159,169,146,50,77,160,75,170,144,48,79,178,164,155,59,80,179,162,153,57,78,177,163,154,58,174,82,167,151,55,152,175,83,165,56,176,81,166,150,54,304,308,306,310,85,203,20,186,26,86,201,18,187,24,84,202,19,188,25,199,88,23,189,29,200,21,190,27,89,198,87,22,191,28,91,15,194,184,32,92,16,192,185,30,90,17,193,183,31,14,94,197,180,35,181,12,95,195,33,13,93,196,182,34,309,315,316,307 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 321 = 1 + 5*64, 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#fdf5f382e471d95c048f9fa2e9b8340aa5eb614276b1c155a6fb7129b8435eb8, M = {60} 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, 64): MacNeish's product over GF(64); GF(64) = F_2[x]/(x^6 + 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: 21.

last edited by qawbecrdtey at 2026-10-01 23:04:49 · history