Equation 677 Database

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Magma 98993818a6e1…

magma 98993818a6e1
Size
321
Isomorphism class hash
98993818a6e19d6a412b403a58923183f74509958fd4af81e43522fec954b396
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 22:32:04
Display reorder
300,194,34,168,136,190,192,35,169,137,191,193,33,170,135,189,30,197,171,132,186,31,195,133,187,172,134,32,196,173,188,200,25,174,142,181,198,26,175,143,182,199,24,176,141,180,28,203,177,138,184,29,201,178,139,185,27,202,179,140,183,303,307,315,312,262,1,263,261,260,253,0,254,252,255,257,2,258,256,259,3,273,274,272,275,4,264,265,267,266,269,5,268,270,271,284,6,286,285,287,277,7,278,276,279,280,8,282,281,283,9,296,298,297,299,10,289,290,288,291,11,293,294,292,295,318,317,319,320,149,42,92,242,206,147,43,90,240,204,148,44,91,241,205,45,145,95,245,209,46,146,243,207,93,244,47,144,94,208,155,40,87,248,212,153,41,88,246,210,154,39,89,247,211,36,151,86,251,215,37,152,84,249,213,38,150,85,250,214,316,302,306,311,56,157,97,69,19,54,158,98,70,20,55,156,96,71,18,160,59,100,68,22,161,57,66,23,101,67,159,58,99,21,51,163,103,60,17,52,164,104,61,15,53,162,102,62,16,166,50,106,63,13,167,48,107,64,14,165,49,105,65,12,308,310,305,314,230,74,121,109,223,228,72,122,110,224,229,73,120,108,222,77,233,124,112,226,75,231,113,227,125,111,76,232,123,225,236,80,127,115,221,234,78,128,116,219,235,79,126,114,220,83,239,130,118,217,81,237,131,119,218,82,238,129,117,216,309,304,301,313 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#514dffc0e0e0286a01e02cffb6912c439b28b51da818e57a2690264fae383974, 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 22:32:05 · history