Equation 677 Database

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Magma 56a4b056362e…

magma 56a4b056362e
Size
321
Isomorphism class hash
56a4b056362ea1ece2b02e74b5c7afbc79c14ac0b202cfa6c96b35871d3940f3
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 22:51:00
Display reorder
318,238,237,239,236,234,235,228,229,230,231,232,233,253,45,184,133,46,134,254,185,47,132,252,183,44,136,256,180,42,137,257,181,43,135,255,182,190,36,139,259,191,37,140,260,189,38,138,258,39,186,142,262,40,187,143,263,41,188,141,261,300,312,316,307,81,83,82,79,80,78,74,72,73,77,75,76,49,94,64,4,95,5,50,65,93,3,48,63,90,1,52,60,91,0,53,61,92,2,51,62,70,85,10,55,71,86,11,56,69,84,9,54,88,66,6,58,89,67,7,59,87,68,8,57,313,317,320,319,195,197,196,193,194,192,203,201,202,199,200,198,105,274,248,153,275,154,106,246,273,155,107,247,270,152,104,251,271,150,102,249,272,151,103,250,243,265,144,96,244,266,145,97,245,264,146,98,268,242,147,99,269,240,148,100,267,241,149,101,303,315,310,314,282,284,283,287,285,286,279,280,281,278,276,277,213,158,109,13,156,14,214,110,157,12,215,108,161,16,212,112,159,17,210,113,160,15,211,111,115,164,19,204,116,162,20,205,114,163,18,206,167,118,22,207,165,119,23,208,166,117,21,209,302,304,311,309,168,170,169,173,171,172,176,174,175,179,177,178,122,296,222,25,294,26,120,223,295,24,121,224,299,28,125,225,297,29,123,226,298,27,124,227,220,291,31,128,221,292,32,126,219,293,30,127,290,216,34,131,288,217,35,129,289,218,33,130,301,305,306,308 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#b8dd5d8f5072bb4839777555438d548fef97075a280814a177ddbc224cea50a0, M = {61} 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 22:51:01 · history