Equation 677 Database

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Magma 23f56b626b90…

magma 23f56b626b90
Size
321
Isomorphism class hash
23f56b626b90a0a4f19798d18528107f9f6588dcda4ae7ded128ae6141a31cae
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 22:45:03
Display reorder
300,208,34,80,213,39,209,40,35,78,214,33,41,207,79,215,38,204,30,76,212,36,205,31,77,210,37,206,32,75,211,240,25,199,45,242,26,200,46,244,246,24,198,47,249,250,202,28,44,74,218,203,29,42,72,216,201,27,43,73,217,314,315,302,305,265,264,266,267,11,268,9,269,270,271,273,10,272,274,275,7,260,261,262,263,8,252,253,254,255,6,256,257,258,259,291,288,289,2,290,292,293,1,295,294,296,297,0,299,298,285,284,5,286,287,277,276,3,278,279,281,280,4,282,283,319,317,318,320,181,12,153,189,87,182,88,13,154,190,14,89,180,155,191,90,184,15,152,188,91,185,16,150,186,92,183,17,151,187,159,18,179,85,195,19,177,86,160,196,20,178,84,161,197,175,21,81,158,194,176,22,82,156,192,174,23,83,157,193,307,311,309,310,164,236,225,96,144,162,145,234,226,97,235,146,163,227,98,147,167,232,228,99,148,165,233,229,100,149,166,231,230,101,223,243,170,142,241,247,168,143,224,245,251,169,141,222,248,173,238,138,219,93,171,239,139,220,94,172,237,140,221,95,303,313,306,316,48,123,113,129,63,49,64,124,111,130,125,65,50,112,131,62,51,122,109,128,60,52,120,110,126,61,53,121,108,127,104,114,54,69,135,115,55,70,102,136,116,56,71,103,137,57,117,68,107,134,58,118,66,105,132,59,119,67,106,133,301,304,312,308 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#8cce333a947232ca69e33881346ef6b490f8a5c022184a0ee2c46fc59b5e71a5, 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 22:45:04 · history