Equation 677 Database

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Magma 8579f68c441a…

magma 8579f68c441a
Size
321
Isomorphism class hash
8579f68c441ad010f6716d9c4efa51bb2c2291130999a0e69539c2e4b3fbd7e7
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 22:33:34
Display reorder
300,144,190,100,67,120,145,191,101,68,118,146,189,99,66,119,186,143,97,63,123,187,142,98,64,121,188,232,229,65,122,136,181,92,59,115,137,182,93,60,116,138,180,91,58,117,184,139,95,61,114,185,140,96,62,113,183,141,94,226,231,306,303,315,307,247,295,293,292,294,248,299,297,296,298,246,291,289,288,290,279,250,277,276,278,283,251,281,280,282,287,249,284,285,286,245,259,256,257,258,243,263,261,260,262,244,255,252,253,254,271,241,268,269,270,275,242,272,273,274,267,240,264,265,266,319,318,320,317,12,157,56,169,235,225,158,57,167,178,11,156,55,168,179,153,15,52,165,176,154,13,53,166,177,155,14,54,164,175,18,148,47,161,172,16,149,48,159,170,17,147,46,160,171,151,21,50,163,174,152,19,51,162,173,150,20,49,233,234,301,302,311,304,31,111,197,212,77,32,112,198,213,78,33,110,199,211,79,107,30,200,208,76,108,28,201,209,74,109,29,202,210,75,22,103,195,204,69,23,104,196,205,70,24,102,194,203,71,106,25,192,237,72,230,26,236,207,227,105,27,193,206,73,316,312,308,309,125,218,80,36,4,126,219,81,34,5,124,217,82,35,6,214,128,83,39,3,215,129,84,37,2,216,127,85,38,1,131,222,86,42,8,132,223,87,40,9,130,221,88,41,10,220,134,89,45,224,239,135,228,43,7,238,133,90,44,0,305,310,314,313 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#61e4460e7132ae46985bdc51b44ba41f1d8967bba1a2e054d2c046422600ec54, 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 22:33:35 · history