Equation 677 Database

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Magma 2adb0edc3bf0…

magma 2adb0edc3bf0
Size
381
Isomorphism class hash
2adb0edc3bf085214bbbf61e56ca14b5c56eba62c71a3071d6f6964a6ccf3f0e
Satisfies Equation 255
yes
Right-cancellative
yes
Idempotent
no
Fiber matrix
symmetric: yes · normal: yes · rank: 1 (nullity 380) what is this?
Submitted by
qawbecrdtey
Submitted at
2026-10-01 23:40:29
Display reorder
380,213,222,218,208,196,202,238,225,230,253,243,248,6,293,7,73,78,68,103,98,298,93,83,88,173,178,168,188,193,183,18,288,13,28,33,22,268,256,260,283,273,278,324,325,326,327,328,329,118,113,108,128,133,123,138,148,143,163,153,158,63,53,58,48,43,38,357,348,378,373,343,363,353,338,331,367,211,221,216,205,195,200,236,227,233,252,241,246,0,291,1,70,75,65,100,95,296,90,81,86,170,175,166,185,190,181,17,287,12,27,32,20,267,259,263,280,271,276,315,316,317,312,313,314,115,110,105,127,131,122,137,147,142,162,152,157,61,51,56,45,40,36,359,345,376,370,341,360,351,337,332,366,212,223,217,207,197,203,237,226,232,251,242,247,3,290,2,71,76,66,101,96,295,91,80,85,172,177,167,187,192,182,15,285,11,25,30,24,266,258,264,281,270,275,306,307,308,309,310,311,116,111,106,126,132,121,135,145,140,161,150,156,60,50,55,46,41,35,355,346,375,371,340,361,350,335,330,365,210,220,215,206,198,201,235,228,231,250,240,245,5,292,4,72,77,67,102,97,297,92,82,87,171,176,165,186,191,180,16,286,10,26,31,21,265,257,262,282,272,277,301,300,302,303,304,305,117,112,107,125,130,120,136,146,141,160,151,155,62,52,57,47,42,37,356,347,377,372,342,362,352,336,333,368,214,224,219,209,199,204,239,229,234,254,244,249,8,294,9,74,79,69,104,99,299,94,84,89,174,179,169,189,194,184,19,289,14,29,34,23,269,255,261,284,274,279,319,320,318,322,323,321,119,114,109,129,134,124,139,149,144,164,154,159,64,54,59,49,44,39,358,349,379,374,344,364,354,339,334,369 history
Raw table
canonical order · displayed order
Equational Theories
Finite Magma Explorer

Commentary

Order 381 = 1 + 5*76, 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#b1a8d3ba3db58654b282150679ccf1b928926281c9ba708fe38c950723e6a1aa, M = {68} 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, 76): MacNeish's product over GF(4) x GF(19); GF(4) = F_2[x]/(x^2 + 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: 51.

last edited by qawbecrdtey at 2026-10-01 23:40:30 · history