Equation 677 Database

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Magma 596cc6261ea4…

magma 596cc6261ea4
Size
321
Isomorphism class hash
596cc6261ea4e472292431ab11aa3040976efa1fec411bb0f33927c75fe1e91a
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 22:59:32
Display reorder
312,234,252,256,275,17,88,99,223,18,89,100,222,15,87,102,220,16,86,101,221,233,251,257,274,105,11,81,216,103,12,82,217,104,10,83,215,14,107,84,219,232,258,250,273,13,106,85,218,189,190,188,185,186,187,191,192,291,289,290,292,306,304,308,317,294,283,278,277,205,74,28,9,206,75,29,8,209,73,30,5,207,71,31,6,208,72,32,7,33,211,79,0,279,295,284,276,34,210,80,1,214,35,78,3,212,36,76,4,213,37,77,2,184,182,183,180,181,179,175,173,177,178,176,174,310,301,305,315,24,95,170,69,25,96,169,70,236,254,271,249,26,97,172,68,237,255,272,248,27,98,171,67,166,22,93,62,167,23,94,63,168,21,92,64,235,270,253,247,19,164,90,65,20,165,91,66,158,159,160,161,162,163,156,157,287,293,286,288,302,319,303,316,280,282,281,285,40,58,51,111,41,59,50,110,238,246,243,259,38,60,53,108,39,61,52,109,49,44,57,115,242,240,245,261,48,45,56,114,43,46,54,112,42,47,55,113,239,241,244,260,195,193,194,198,196,197,201,199,203,204,202,200,300,309,307,318,121,151,141,131,122,152,142,132,120,150,140,130,124,154,144,134,125,155,145,135,123,153,143,133,267,263,269,265,266,262,268,264,139,119,149,129,117,137,147,127,118,138,148,128,116,136,146,126,224,225,226,227,228,229,230,231,298,296,297,299,314,313,311,320 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#e051b0f30a8ed34180a71689094d032915fc358f2733da2908c1415c24d3cdbe, 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 22:59:33 · history