Equation 677 Database

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Magma 7b0a8f9a9d7a…

magma 7b0a8f9a9d7a
Size
321
Isomorphism class hash
7b0a8f9a9d7a0647d8c452ea90c542e3561b02438f9a53d03a63c2bb0911ef2d
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 22:50:53
Display reorder
300,118,97,39,141,121,40,119,142,122,98,96,117,41,143,120,38,100,114,140,124,101,36,115,138,125,37,99,116,139,123,45,109,103,132,127,46,110,104,133,128,47,108,102,134,126,112,44,106,135,130,113,42,107,136,131,111,43,105,137,129,303,301,311,313,291,290,244,289,288,245,295,292,293,294,298,299,243,296,297,240,286,287,284,285,278,241,279,276,277,242,282,283,280,281,250,255,254,252,253,251,259,258,257,256,249,263,262,261,260,267,246,266,265,264,271,247,270,268,269,275,248,274,272,273,318,320,319,317,235,156,48,22,178,49,237,23,179,157,158,239,50,21,177,51,159,233,18,174,160,52,229,19,175,53,161,231,20,176,54,217,162,13,169,55,219,163,14,170,56,220,164,12,168,222,57,165,16,172,224,58,166,17,173,226,59,167,15,171,312,302,309,316,189,73,3,67,153,4,190,68,154,74,72,191,5,66,155,2,76,188,70,152,77,1,186,71,150,0,75,187,69,151,9,180,79,65,144,10,181,80,63,145,11,182,78,64,146,183,8,82,61,147,184,6,83,62,148,185,7,81,60,149,306,304,307,314,197,85,25,234,213,26,195,236,214,86,84,196,24,238,215,28,88,193,232,212,89,29,194,228,210,27,87,192,230,211,31,203,91,216,204,32,201,92,218,205,30,202,90,221,206,199,34,94,223,207,200,35,95,225,208,198,33,93,227,209,310,308,305,315 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#b88a5e69f4f2e8155017edd6b5c4ba2f90c1abf217fa4fb1e3b057bac30e1168, 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 22:50:54 · history