Equation 677 Database

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Magma fde005a33806…

magma fde005a33806
Size
321
Isomorphism class hash
fde005a33806f98356a362ad560ce2f9cfeac3c2382c343bfab0419a5a44ce6d
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 22:27:21
Display reorder
300,233,178,101,167,244,99,231,165,245,179,100,177,232,166,243,97,229,174,163,240,98,230,175,164,241,96,228,176,162,242,169,158,239,107,250,170,156,237,105,251,168,157,238,106,249,161,172,235,103,246,159,173,236,104,247,102,160,171,234,248,315,311,304,303,268,269,0,270,271,2,272,274,275,273,1,265,264,267,266,4,252,253,254,255,5,256,257,258,259,3,260,261,263,262,292,294,293,7,295,297,299,296,8,298,288,291,289,6,290,278,276,277,10,279,282,280,281,11,283,9,286,285,284,287,318,317,319,320,61,56,82,189,220,83,62,190,221,54,81,55,60,191,219,78,64,59,188,216,79,65,57,186,217,80,63,58,187,218,51,180,67,73,226,52,181,68,74,227,53,182,66,72,225,183,50,70,76,222,184,48,71,77,223,75,185,49,69,224,308,314,316,301,125,114,30,196,211,31,123,197,212,115,32,116,124,195,210,33,121,117,192,214,34,122,118,193,215,35,120,119,194,213,112,202,131,28,209,113,203,129,29,207,111,201,130,27,208,198,108,127,24,205,199,109,128,25,206,26,200,110,126,204,302,313,306,310,140,36,12,85,145,13,138,86,146,37,14,38,139,84,144,15,143,39,88,148,16,141,40,89,149,17,142,41,87,147,42,91,135,18,151,43,92,136,19,152,44,90,137,20,150,94,45,134,21,154,95,46,132,22,155,23,93,47,133,153,305,312,307,309 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#3519a427d5ae28e51e8dce355af6af1aa210384ac7088475411fc50e96b55163, 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 22:27:22 · history