Equation 677 Database

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Magma 436573313d31…

magma 436573313d31
Size
321
Isomorphism class hash
436573313d31cb54491b4dee05bbd227f6dd49538294a50053493989e0e4ed22
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 22:51:12
Display reorder
300,66,94,145,32,129,67,33,95,146,130,68,34,93,144,131,35,65,91,141,132,36,64,92,142,133,37,226,229,143,134,136,100,58,38,127,137,101,59,39,128,135,99,60,40,126,96,139,61,41,124,97,140,62,42,125,98,138,63,224,232,307,302,314,301,248,299,298,296,297,246,288,290,291,289,247,292,294,295,293,280,251,283,282,281,284,249,287,286,285,276,250,278,279,277,262,263,243,260,261,255,254,244,252,253,258,259,245,256,257,275,274,242,273,272,267,266,240,265,264,270,271,241,269,268,320,319,317,318,79,202,158,105,236,227,106,200,156,189,78,107,201,157,190,104,75,198,154,187,102,76,199,155,188,103,77,197,153,186,149,193,70,110,183,147,191,71,111,181,148,192,69,112,182,196,152,73,109,185,194,150,74,108,184,195,151,72,230,235,306,303,310,313,8,160,213,123,90,6,121,161,211,88,7,122,159,212,89,119,11,163,209,86,120,9,164,210,87,118,10,162,208,85,205,166,3,115,82,203,167,4,113,80,204,165,5,114,81,168,207,2,117,228,169,237,1,231,83,233,206,0,116,84,316,305,304,311,46,21,17,219,180,47,217,22,18,178,48,218,20,19,179,215,49,24,16,176,216,50,25,14,177,214,51,23,15,175,45,27,52,223,172,43,28,53,221,170,44,26,54,222,171,30,12,55,239,174,31,225,56,238,234,29,13,57,220,173,315,312,309,308 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#ba7c5b5fc3c8b2f23fa53f03c835320f8b0f039ca1c741e1670481476e08a637, 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 22:51:13 · history