Equation 677 Database

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Magma b90b9d552992…

magma b90b9d552992
Size
321
Isomorphism class hash
b90b9d5529929fcf1f28b69f6785a548e73c271943f472069fd6fb170968b623
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 23:03:46
Display reorder
300,24,151,230,95,241,93,152,25,228,242,150,94,26,229,240,27,91,154,233,244,28,92,155,231,245,29,90,153,232,243,149,30,86,236,247,147,31,84,234,248,148,32,85,235,246,145,33,89,239,250,34,146,87,237,251,35,144,88,238,249,302,304,315,313,258,257,259,10,256,11,260,261,262,263,252,9,253,254,255,268,6,269,270,271,273,7,272,274,275,264,8,265,266,267,281,280,0,282,283,285,284,2,286,287,276,277,1,278,279,292,293,4,294,295,296,297,5,298,299,289,288,3,290,291,318,320,317,319,158,103,109,45,205,46,104,156,110,206,102,47,157,108,204,161,44,106,112,208,159,42,107,113,209,160,43,105,111,207,101,164,36,115,211,99,162,37,116,212,100,163,38,114,210,97,167,39,118,214,165,98,40,119,215,166,96,41,117,213,316,301,309,312,121,217,59,73,140,74,218,122,57,138,216,72,120,58,139,124,76,220,55,143,125,77,221,56,141,123,75,219,54,142,223,127,79,50,135,224,128,80,48,136,222,126,78,49,137,226,130,82,53,134,131,227,83,51,132,129,225,81,52,133,303,310,308,311,175,182,193,68,14,66,180,176,194,12,181,67,174,192,13,178,71,185,196,17,179,69,183,197,15,177,70,184,195,16,188,173,63,199,20,186,171,64,200,18,187,172,65,198,19,191,169,62,202,23,170,189,60,203,21,168,190,61,201,22,305,307,306,314 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#f3708acaf97ab90d0e627f94c9229dfefc0b06412aed9a05696d0ed9b4a78cdc, 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 23:03:47 · history