Equation 677 Database

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Magma f009bf63b24e…

magma f009bf63b24e
Size
321
Isomorphism class hash
f009bf63b24e8398656c894f86cf0a79d3dd2c95b9f0b085a78dba20a9254202
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 22:44:55
Display reorder
300,76,71,180,111,97,69,98,77,181,112,96,70,75,179,110,67,93,72,176,114,94,68,73,177,115,95,66,74,178,113,103,62,82,246,245,104,60,83,250,248,105,102,61,81,185,65,99,78,182,107,183,63,100,79,108,64,101,80,184,106,314,313,301,311,269,268,270,271,25,273,26,272,274,275,24,264,265,267,266,253,28,252,254,255,29,257,256,258,259,27,261,260,263,262,31,292,293,294,295,32,297,296,299,298,290,30,288,289,291,276,34,277,278,279,282,281,35,280,283,285,33,284,286,287,318,319,317,320,120,136,226,214,9,134,10,121,227,215,11,135,119,225,213,139,8,116,222,210,6,137,117,223,211,7,138,118,224,212,1,131,126,232,220,0,132,127,233,221,219,2,133,125,231,130,3,122,228,216,229,128,4,123,217,129,5,124,230,218,307,310,304,303,149,239,91,16,43,237,44,150,92,17,42,238,151,90,15,235,46,148,87,12,47,236,146,88,13,45,234,147,89,14,41,247,140,244,22,39,251,141,249,23,21,40,243,142,109,241,37,143,85,18,86,242,38,144,19,240,36,145,84,20,302,315,308,316,202,195,168,161,58,196,59,203,169,162,57,197,201,167,163,194,54,198,164,160,55,192,199,165,158,56,193,200,166,159,49,186,208,174,152,50,187,209,175,153,154,48,188,207,173,189,52,204,170,155,171,190,53,205,156,191,51,206,172,157,312,305,306,309 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#87aba77d55a93960597d69a42bda986d959be94fa8d2c920629e2ba026b38a72, 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 22:44:56 · history