Equation 677 Database

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Magma 711d449c7858…

magma 711d449c7858
Size
321
Isomorphism class hash
711d449c7858df087e0e46ae0c51566ce74a1a268a72f3401596801f9ad3935d
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 22:59:56
Display reorder
300,76,193,33,146,206,77,34,144,204,194,75,192,35,145,205,149,32,72,196,209,30,73,197,147,207,31,74,195,148,208,24,199,82,152,212,25,200,83,150,210,26,198,81,151,211,202,27,78,155,215,203,28,79,153,213,201,29,80,154,214,303,302,311,307,262,263,251,261,260,253,249,252,255,254,257,258,250,256,259,272,247,273,274,275,248,264,266,265,267,246,269,270,268,271,242,286,284,285,287,240,278,276,277,279,241,282,280,281,283,298,245,296,297,299,290,243,289,288,291,294,244,292,293,295,320,318,317,319,238,239,4,104,88,234,5,102,89,235,236,237,3,103,87,107,1,230,231,84,0,233,232,105,85,2,228,229,106,86,10,221,220,99,94,11,217,216,100,95,9,219,218,101,93,227,6,226,98,90,223,7,222,96,91,225,8,224,97,92,301,305,313,314,52,172,117,163,182,53,118,164,180,173,51,171,119,162,181,166,116,48,168,185,114,49,169,167,183,115,50,170,165,184,108,178,58,161,188,109,179,59,159,186,110,177,57,160,187,174,111,54,157,191,175,112,55,158,189,176,113,56,156,190,304,308,309,312,139,60,39,122,12,140,40,120,13,61,138,62,41,121,14,125,38,142,63,15,36,143,64,123,16,37,141,65,124,17,45,66,137,128,18,46,67,135,126,19,47,68,136,127,20,69,44,133,131,21,70,42,134,129,22,71,43,132,130,23,310,316,315,306 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#e6ff3ea71fab369083c7c0ebcc1e5818a214c988729d733a41fa2a4b44566c90, 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 22:59:57 · history